Finite Element Method for Solving Poisson's Equation

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MATLAB Implementation of Finite Element Method for Poisson's Equation - A Computational Program with Numerical Analysis and Visualization Capabilities

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This document presents the implementation of the finite element method for solving Poisson's equation, a numerical computational approach applicable to various practical engineering problems. The method employs MATLAB programming, utilizing key computational algorithms including mesh generation using the delaunayTriangulation function, finite element assembly through sparse matrix operations, and boundary condition handling via Dirichlet or Neumann constraint implementations. The program efficiently computes numerical solutions using linear or quadratic basis functions and incorporates visualization tools like pdeplot for result analysis. This MATLAB implementation enables comprehensive understanding of finite element discretization, stiffness matrix formulation, and error estimation techniques, providing valuable insights for further research and practical applications in computational mathematics and engineering simulations.

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