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

E. Burman & B. Stamm

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 = {E. Burman and B. Stamm}, 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 AU - E. Burman & B. Stamm 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 and B. Stamm. (2009). Local Discontinuous Galerkin Method with Reduced Stabilization for Diffusion Equations. Communications in Computational Physics. 5 (2-4). 498-514. doi:
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