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Volume 7, Issue 3
Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems

Sebastian Franz & H.-G. Roos

DOI: 10.4208/nmtma.2014.1320nm

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 356-373.

Published online: 2014-07

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  • Abstract

In this paper we present a first supercloseness analysis for higher-order Galerkin FEM applied to a singularly perturbed convection-diffusion problem. Using a solution decomposition and a special representation of our finite element space, we are able to prove a supercloseness property of $p + 1/4$ in the energy norm where the polynomial order $p ≥ 3$ is odd.

  • Keywords

Singular perturbation, layer-adapted meshes, superconvergence, postprocessing

  • AMS Subject Headings

65N12, 65N30, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-7-356, author = {Sebastian Franz and H.-G. Roos}, title = {Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {3}, pages = {356--373}, abstract = {

In this paper we present a first supercloseness analysis for higher-order Galerkin FEM applied to a singularly perturbed convection-diffusion problem. Using a solution decomposition and a special representation of our finite element space, we are able to prove a supercloseness property of $p + 1/4$ in the energy norm where the polynomial order $p ≥ 3$ is odd.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.1320nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5879.html} }
TY - JOUR T1 - Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems AU - Sebastian Franz & H.-G. Roos JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 356 EP - 373 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.1320nm UR - https://global-sci.org/intro/article_detail/nmtma/5879.html KW - Singular perturbation, layer-adapted meshes, superconvergence, postprocessing AB -

In this paper we present a first supercloseness analysis for higher-order Galerkin FEM applied to a singularly perturbed convection-diffusion problem. Using a solution decomposition and a special representation of our finite element space, we are able to prove a supercloseness property of $p + 1/4$ in the energy norm where the polynomial order $p ≥ 3$ is odd.

Sebastian Franz and H.-G. Roos. (2014). Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems. Numerical Mathematics: Theory, Methods and Applications. 7 (3). 356-373. doi:10.4208/nmtma.2014.1320nm
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