Volume 5, Issue 2-4
Local Discontinuous Galerkin Method with Reduced Stabilization for Diffusion Equations

E. Burman & B. Stamm

DOI:

Commun. Comput. Phys., 5 (2009), pp. 498-514.

Published online: 2009-02

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  • Abstract

We extend the results on minimal stabilization of Burmanand Stamm [J. Sci. Comp., 33 (2007), pp. 183-208] to the case of the local discontinuous Galerkin methods on mixed form. The penalization term on the faces is relaxed to act only on a part of the polynomial spectrum. Stability in the form of a discrete inf-sup condition is proved and optimal convergence follows. Some numerical examples using high order approximation spaces illustrate the theory. 

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@Article{CiCP-5-498, author = {}, title = {Local Discontinuous Galerkin Method with Reduced Stabilization for Diffusion Equations}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {2-4}, pages = {498--514}, abstract = {

We extend the results on minimal stabilization of Burmanand Stamm [J. Sci. Comp., 33 (2007), pp. 183-208] to the case of the local discontinuous Galerkin methods on mixed form. The penalization term on the faces is relaxed to act only on a part of the polynomial spectrum. Stability in the form of a discrete inf-sup condition is proved and optimal convergence follows. Some numerical examples using high order approximation spaces illustrate the theory. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7746.html} }
TY - JOUR T1 - Local Discontinuous Galerkin Method with Reduced Stabilization for Diffusion Equations JO - Communications in Computational Physics VL - 2-4 SP - 498 EP - 514 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7746.html KW - AB -

We extend the results on minimal stabilization of Burmanand Stamm [J. Sci. Comp., 33 (2007), pp. 183-208] to the case of the local discontinuous Galerkin methods on mixed form. The penalization term on the faces is relaxed to act only on a part of the polynomial spectrum. Stability in the form of a discrete inf-sup condition is proved and optimal convergence follows. Some numerical examples using high order approximation spaces illustrate the theory. 

E. Burman & B. Stamm. (2020). Local Discontinuous Galerkin Method with Reduced Stabilization for Diffusion Equations. Communications in Computational Physics. 5 (2-4). 498-514. doi:
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