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Computational Methods in Applied Sciences, Volume 16: Partial Differential Equations: Modelling and Numerical Simulation

Partial Differential Equations: Modelling and Numerical Simulation (Computational Methods in Applied Sciences) (Computational Methods in Applied Sciences)

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Computational Methods in Applied Sciences, Volume 16: Partial Differential Equations: Modelling and Numerical Simulation

Partial Differential Equations: Modelling and Numerical Simulation (Computational Methods in Applied Sciences) (Computational Methods in Applied Sciences)

4.85 32,210 ratings · 2,512 reviews
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Overview: This book is dedicated to Olivier Pironneau.For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schr dinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity.Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analysis of partial differential equations.The first part is devoted to discontinuous Galerkin and mixed finite element methods, both methodologies of fast growing popularity. They are applied to a variety of linear and nonlinear problems, including the Stokes problem from fluid mechanics and fully nonlinear elliptic equations of the Monge-Amp re type. Numerical methods for linear and nonlinear hyperbolic problems are discussed in the second part. The third part is concerned with domain decomposition methods, with applications to scattering problems for wave models and to electronic structure computations.The next part is devoted to the numerical simulation of problems in fluid mechanics that involve free surfaces and moving boundaries. The finite difference solution of a problem from spectral geometry has also been included in this part. Inverse problems are known to be efficient models used in geology, medicine, mechanics and many other natural sciences. New results in this field are presented in the fifth part.The final part of the book is addressed to another rapidly developing area in applied mathematics, namely, financial mathematics. The reader will find in this final part of the volume recent results concerning the simulation of finance related processes modeled by parabolic variational inequalities.

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Published July 7, 2008
ISBN 4230984
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Roland Glowinski writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Roland Glowinski lives with their spouse and a very vocal rescue cat.

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Margaret Adams
Margaret Adams October 29, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
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Lisa Allen June 25, 2024
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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Jennifer King October 12, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Brian Perez
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Jessica Baker
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Jacob Thomas
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
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I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
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Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Andrew Moore
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Rebecca Lee
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Mark Carter May 11, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Edward Turner
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Elizabeth Adams
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Kimberly Nelson
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Charles Turner
Charles Turner December 05, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Cynthia Garcia
Cynthia Garcia March 14, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Ashley Thomas
Ashley Thomas June 28, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Michelle Brown
Michelle Brown January 06, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Jessica Edwards
Jessica Edwards October 08, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Edward Turner
Edward Turner November 02, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Margaret Carter
Margaret Carter January 23, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Joshua Jones
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Cynthia Garcia
Cynthia Garcia October 13, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Karen Turner
Karen Turner December 03, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Kimberly Young
Kimberly Young May 19, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Joseph Lopez
Joseph Lopez January 29, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Ashley White
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Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
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Kevin Torres February 17, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Mark Gomez
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Linda Johnson
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Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Rebecca Evans
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
Thomas Nguyen
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Laura Collins
Laura Collins September 08, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Sarah  Davis
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Dorothy Wilson
Dorothy Wilson November 19, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Steven Hill
Steven Hill December 09, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Robert Jones
Robert Jones March 30, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Jennifer Gonzalez
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
David Anderson
David Anderson May 13, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Jennifer Turner
Jennifer Turner June 23, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Steven Hill
Steven Hill June 09, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Andrew Thomas
Andrew Thomas October 25, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Patricia Gonzalez
Patricia Gonzalez September 10, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Rebecca Wilson
Rebecca Wilson January 12, 2024
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Deborah Hernandez
Deborah Hernandez April 12, 2025
An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Unlikely to reread, but a reasonable expenditure of time.
Michelle King
Michelle King May 21, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Charles Turner
Charles Turner September 10, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Amanda Smith
Amanda Smith November 16, 2025
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Gary Taylor
Gary Taylor December 16, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Dorothy King
Dorothy King February 03, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Rebecca Evans
Rebecca Evans August 16, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
William Baker
William Baker August 01, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Dorothy Phillips
Dorothy Phillips February 25, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Melissa Lewis
Melissa Lewis August 07, 2024
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
Carol Harris
Carol Harris December 21, 2024
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average.
Sandra Miller
Sandra Miller August 01, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Deborah Campbell
Deborah Campbell May 26, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Joshua Green
Joshua Green September 03, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Eric Thompson
Eric Thompson August 22, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Mark Diaz
Mark Diaz October 22, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Susan Williams
Susan Williams March 08, 2024
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
Mark Thomas
Mark Thomas January 18, 2024
An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
Rebecca Thomas
Rebecca Thomas February 15, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Jacob Green
Jacob Green February 04, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Amanda Collins
Amanda Collins August 12, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
David  Davis
David Davis February 15, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Carol Phillips
Carol Phillips August 14, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Kevin Young
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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Mark Hall
Mark Hall August 18, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
George Hernandez
George Hernandez November 16, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
David Walker
David Walker March 08, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Laura Gonzalez
Laura Gonzalez July 12, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
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