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Volume 19, Issue 1
Finite Element Approximation of a Nonlinear Steady-State Heat Conduction Problem

Michal Křížek

J. Comp. Math., 19 (2001), pp. 27-34.

Published online: 2001-02

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  • Abstract

We examine a nonlinear partial differential equation of elliptic type with the homogeneous Dirichlet boundary conditions. We prove comparison and maximum principles. For associated finite element approximations we introduce a discrete analogue of the maximum principle for linear elements, which is based on nonobtuse tetrahedral partitions.

  • Keywords

Boundary value elliptic problems, Comparison principle, Maximum principle, Finite element method, Discrete maximum principle, Nonobtuse partitions.

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-27, author = {Křížek , Michal}, title = {Finite Element Approximation of a Nonlinear Steady-State Heat Conduction Problem}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {1}, pages = {27--34}, abstract = {

We examine a nonlinear partial differential equation of elliptic type with the homogeneous Dirichlet boundary conditions. We prove comparison and maximum principles. For associated finite element approximations we introduce a discrete analogue of the maximum principle for linear elements, which is based on nonobtuse tetrahedral partitions.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8954.html} }
TY - JOUR T1 - Finite Element Approximation of a Nonlinear Steady-State Heat Conduction Problem AU - Křížek , Michal JO - Journal of Computational Mathematics VL - 1 SP - 27 EP - 34 PY - 2001 DA - 2001/02 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8954.html KW - Boundary value elliptic problems, Comparison principle, Maximum principle, Finite element method, Discrete maximum principle, Nonobtuse partitions. AB -

We examine a nonlinear partial differential equation of elliptic type with the homogeneous Dirichlet boundary conditions. We prove comparison and maximum principles. For associated finite element approximations we introduce a discrete analogue of the maximum principle for linear elements, which is based on nonobtuse tetrahedral partitions.

Křížek , Michal. (2001). Finite Element Approximation of a Nonlinear Steady-State Heat Conduction Problem. Journal of Computational Mathematics. 19 (1). 27-34. doi:
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