Guide The numerical solution of elliptic equations

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Journal of the Society for Industrial and Applied Mathematics

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Numerically solving an elliptic partial differential equation often requires solving a very large, but sparse, linear system. This notebook contains an example in which InterCall is used to solve a PDE by accessing a public domain library to handle the sparse linear system. Arbitrary two-dimensional regions including holes and cracks as well as rectangular three dimensional regions can also be handled with this technique.

However, sometimes it is believed that understanding and applying the full power of wavelets needs a strong mathematical background in functional analysis and approximation theory.

The main idea of this book is to introduce the main concepts and results of wavelet methods for solving linear elliptic partial differential equations in a framework that allows avoiding technicalities to a maximum extend. On the other hand, the book also describes recent research including adaptive methods also for nonlinear problems, wavelets on general domains and applications.

Keywords: wavelets , numerical solution , Galerkin schemes , adaptive methods , elliptic partial differential equations.

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Numerical Methods for Model Parabolic and Elliptic Equations | SpringerLink

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75. Solution of Elliptic Equation - Laplace Equation - Problem#1