Advanced topics in computational partial differential equations

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This book focuses on solving partial differential equations (PDEs), essential for modeling various phenomena across science and technology. With the rise of powerful computers, computational mathematics has evolved from simplified models to complex ones that mirror real-life intricacies. This shift presents challenges in computer science and numerical analysis. The book aims to teach modern, advanced techniques for numerically solving PDEs and introduces models from fields such as finance, medicine, material technology, and geology. A basic understanding of partial differential equations and numerical methods is necessary, along with some knowledge of finite element methods. While familiarity with Diffpack, the programming environment used in examples, is not required, it is beneficial for implementation. The text emphasizes models, methods, and their implementation, utilizing Diffpack for its efficiency in programming PDE solvers and support for advanced numerical techniques. Each chapter includes sections on models and methods, as well as implementation and Diffpack programming, allowing readers to focus on the theoretical aspects if they choose.