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Volume 2, Issue 1
Convergence Analysis of Finite Element Solution of One-Dimensional Singularly Perturbed Differential Equations on Equidistributing Meshes

Weizhang Huang

Int. J. Numer. Anal. Mod., 2 (2005), pp. 57-74.

Published online: 2005-02

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  • Abstract

In this paper convergence on equidistributing meshes is investigated. Equidistributing meshes, or more generally approximate equidistributing meshes, are constructed through the well-known equidistribution principle and a so-called adaptation (or monitor) function which is defined based on estimates on interpolation error for polynomial preserving operators. Detailed convergence analysis is given for finite element solution of singularly perturbed two-point boundary value problems without turning points. Illustrative numerical results are given for a convection-diffusion problem and a reaction-diffusion problem.

  • Keywords

mesh adaptation, equidistribution, error analysis, finite element method.

  • AMS Subject Headings

65M50, 65M60, 65L50, 65L60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-2-57, author = {Huang , Weizhang}, title = {Convergence Analysis of Finite Element Solution of One-Dimensional Singularly Perturbed Differential Equations on Equidistributing Meshes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {1}, pages = {57--74}, abstract = {

In this paper convergence on equidistributing meshes is investigated. Equidistributing meshes, or more generally approximate equidistributing meshes, are constructed through the well-known equidistribution principle and a so-called adaptation (or monitor) function which is defined based on estimates on interpolation error for polynomial preserving operators. Detailed convergence analysis is given for finite element solution of singularly perturbed two-point boundary value problems without turning points. Illustrative numerical results are given for a convection-diffusion problem and a reaction-diffusion problem.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/920.html} }
TY - JOUR T1 - Convergence Analysis of Finite Element Solution of One-Dimensional Singularly Perturbed Differential Equations on Equidistributing Meshes AU - Huang , Weizhang JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 57 EP - 74 PY - 2005 DA - 2005/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/920.html KW - mesh adaptation, equidistribution, error analysis, finite element method. AB -

In this paper convergence on equidistributing meshes is investigated. Equidistributing meshes, or more generally approximate equidistributing meshes, are constructed through the well-known equidistribution principle and a so-called adaptation (or monitor) function which is defined based on estimates on interpolation error for polynomial preserving operators. Detailed convergence analysis is given for finite element solution of singularly perturbed two-point boundary value problems without turning points. Illustrative numerical results are given for a convection-diffusion problem and a reaction-diffusion problem.

Huang , Weizhang. (2005). Convergence Analysis of Finite Element Solution of One-Dimensional Singularly Perturbed Differential Equations on Equidistributing Meshes. International Journal of Numerical Analysis and Modeling. 2 (1). 57-74. doi:
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