Description
Book SynopsisThis text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
Trade Review“This book has a large amount of new exercise problems that are uniformly distributed across the text. … this book is a very nice text which will serve well for the undergraduate as well as graduate students and will also become a ready reference for scholars.” (Murli M. Gupta, Mathematical Reviews, April, 2023)
“Many of the SIAM Review readership will be interested in NMEPPDE from the standpoint of self-study or classroom education. … NMEPPDE offers the applied mathematics reader nearly a single point of entry to our broad and challenging area. … a bit of open space on the bookshelf could profitably be well filled with a copy of NMEPPDE.” (Robert C. Kirby, SIAM Review, Vol. 65 (1), March, 2023)
Table of ContentsFor Example: Modelling Processes in Porous Media with Differential Equations.- For the Beginning: The Finite Difference Method for the Poisson Equation.- The Finite Element Method for the Poisson Equation.- The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order.- Grid Generation and A Posteriori Error Estimation.- Iterative Methods for Systems of Linear Equations.- Beyond Coercivity, Consistency and Conformity.- Mixed and Nonconforming Discretization Methods.- The Finite Volume Method.- Discretization Methods for Parabolic Initial Boundary Value Problems.- Discretization Methods for Convection-Dominated Problems.- An Outlook to Nonlinear Partial Differential Equations.- Appendices.
