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The simplest elliptic boundary value problem is the Poisson problem, given in variational form by ( 2.36 )–( 2.38 ) with \(\varepsilon =1\) , \({\boldsymbol b}={\boldsymbol 0}\) , and \(\sigma =0\) . Finite element methods for computing numerical approximations to this problem are the topic of this chapter. The emphasis is on conforming methods, for which in Sect. 6.1 a brief presentation of the error analysis is provided.

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Finite Element Methods for Diffusion Problems

  • 章节

  • 发表日期：

    2025年

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  • Gabriel R. Barrenechea,
  • Volker John,
  • Petr Knobloch

摘要

The simplest elliptic boundary value problem is the Poisson problem, given in variational form by ( 2.36 )–( 2.38 ) with \(\varepsilon =1\) , \({\boldsymbol b}={\boldsymbol 0}\) , and \(\sigma =0\) . Finite element methods for computing numerical approximations to this problem are the topic of this chapter. The emphasis is on conforming methods, for which in Sect. 6.1 a brief presentation of the error analysis is provided.