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Illustrating the Finite Element Method By Solving Laplace's Equation in Two Dimensions For a Non-Rectangular Region

Frank Kampas
Organization: Physicist at Large Consulting
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The finite element method is the standard approach for solving partial differential equations in geometries in which the boundaries are not simple variable ranges. This article illustrates the basic approach by solving Laplace's equation in two dimensions for a region consisting of two unequal rectangles joined together, for a Dirchlet boundary condition (function specified on the boundary).

*Engineering > Finite Element Methods

Finite Element Method, Laplace's Equation, Calculus of Variations
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Finite_Element_Laplace_Equation.nb (532.7 KB) - Mathematica Notebook