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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 86,986 ratings · 4,520 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
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Roland Glowinski is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Roland Glowinski enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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Joshua Campbell
Joshua Campbell July 06, 2024
A very strong entry. 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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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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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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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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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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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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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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Masterpiece from start to finish. 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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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Joseph Turner
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Ryan Collins
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
William Gomez
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Robert Phillips
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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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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Elizabeth Walker
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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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Sandra Nguyen September 29, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Sandra Harris
Sandra Harris October 11, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Richard  Davis
Richard Davis February 26, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Patricia Gonzalez
Patricia Gonzalez September 07, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Sarah Moore
Sarah Moore December 17, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Elizabeth  Parker
Elizabeth Parker May 16, 2025
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.
Sharon Garcia
Sharon Garcia September 18, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Donna King
Donna King February 09, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Sharon Lewis
Sharon Lewis September 27, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Kenneth  Parker
Kenneth Parker December 27, 2025
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Melissa White
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Jessica Rodriguez
Jessica Rodriguez October 23, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Brian Williams
Brian Williams November 13, 2025
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.
Ryan Cruz
Ryan Cruz January 23, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Emily White
Emily White August 02, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Charles Collins
Charles Collins July 24, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Jennifer Garcia
Jennifer Garcia January 13, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Donna Gonzalez
Donna Gonzalez September 01, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Lisa Cruz
Lisa Cruz June 13, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Amanda Reyes
Amanda Reyes April 24, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Ryan Jackson
Ryan Jackson June 30, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
James Collins
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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Robert Evans
Robert Evans April 07, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Cynthia Smith
Cynthia Smith May 30, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Jennifer Gonzalez
Jennifer Gonzalez June 23, 2025
I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. A fair 3 stars.
Mark  Parker
Mark Parker July 05, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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