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  • 标题:Mixed Finite Element Methods for the Poisson Equation Using Biorthogonal and Quasi-Biorthogonal Systems
  • 本地全文:下载
  • 作者:Bishnu P. Lamichhane
  • 期刊名称:Advances in Numerical Analysis
  • 印刷版ISSN:1687-9562
  • 电子版ISSN:1687-9570
  • 出版年度:2013
  • 卷号:2013
  • DOI:10.1155/2013/189045
  • 出版社:Hindawi Publishing Corporation
  • 摘要:We introduce two three-field mixed formulations for the Poisson equation and propose finite element methods for their approximation. Both mixed formulations are obtained by introducing a weak equation for the gradient of the solution by means of a Lagrange multiplier space. Two efficient numerical schemes are proposed based on using a pair of bases for the gradient of the solution and the Lagrange multiplier space forming biorthogonal and quasi-biorthogonal systems, respectively. We also establish an optimal a priori error estimate for both finite element approximations.
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