Numerical Methods for Elliptic and Parabolic Partial Differential Equations: With contributions by Andreas Rupp

This graduate-level text provides an application-oriented introduction to numerical methods for elliptic and parabolic partial differential equations, covering finite difference, finite element, and finite volume methods. It includes modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises. For students with mathematics majors, it is an excellent introduction to the theory and methods, guiding them in the selection of methods and helping them to understand and pursue finite element programming. For engineering and physics students, it provides a general framework for the formulation and analysis of methods.

Format: Paperback / softback
Length: 802 pages
Publication date: 21 November 2022
Publisher: Springer Nature Switzerland AG

This advanced text, designed for graduate students, offers an application-focused introduction to numerical methods for elliptic and parabolic partial differential equations. It encompasses finite difference, finite element, and finite volume methods, seamlessly integrating theory and applications throughout. The book explores contemporary topics such as adaptive methods, multilevel methods, and techniques for convection-dominated problems, accompanied by detailed illustrations and extensive exercises. For mathematics majors, it serves as an excellent primer on the theory and methodologies, aiding in method selection and facilitating the understanding of finite element programming. For engineering and physics students, it provides a comprehensive framework for formulating and analyzing methods.

In this second edition, the book has been expanded to include additional chapters on mixed discretization, generalizing and unifying known approaches, broader applications on systems of diffusion, convection, and reaction, enhanced chapters on node-centered finite volume methods and methods of convection-dominated problems, specifically focusing on the now-popular cell-centered finite volume method, and the consideration of realistic formulations beyond the Poisson equation for all models and methods.

By providing a comprehensive and up-to-date coverage of numerical methods for elliptic and parabolic partial differential equations, this text serves as a valuable resource for advanced students, researchers, and practitioners in mathematics, engineering, and applied sciences.

Weight: 1240g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030793876
Edition number: 2nd ed. 2021