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This 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.

Numerical Methods for Elliptic and Parabolic Partial Differential Equations

For 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 * The Finite Volume Method * Discretization Methods for Parabolic Initial Boundary Value Problems * Iterative Methods for Nonlinear Equations * Discretization Methods for Convection-Dominated Problems * Appendices