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The Standard Galerkin Method

  • Vidar Thomée
Chapter
  • 435 Downloads
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 25)

Abstract

In this introductory chapter we shall study the standard Galerkin finite element method for the approximate solution of the model initial-boundary value problem for the heat equation,
$$\eqalign{ & u_t - \Delta u = f{\text{ }}in\:{\text{ }}\Omega ,\:{\text{ }}for\:t > 0, \cr & u = 0\:on\:\partial \Omega ,\:for\:t > 0,\:with\:u(\cdot,0) = v\:in\:\Omega \cr} $$
(1.1)
where is a domain in R d with smooth boundary ∂Ω, and where u = u(x, t), u t denotes ∂u/∂t, and \( \Delta = \sum\nolimits_{j = 1}^d {\partial ^2 /\partial x_j^2 } \) the Laplacian.

Keywords

Optimal Order Piecewise Linear Function Plane Domain Interior Vertex Galerkin Finite Element Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Vidar Thomée
    • 1
  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden

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