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Volume 21, Issue 4
A Simple Explanation of Superconvergence for Discontinuous Galerkin Solutions to $\boldsymbol{u_t}$+$\boldsymbol{u_x}$=0

Philip Roe

DOI: 10.4208/cicp.OA-2016-0052

Commun. Comput. Phys., 21 (2017), pp. 905-912.

Published online: 2018-04

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  • Abstract

The superconvergent property of the Discontinuous Galerkin (DG) method for linear hyperbolic systems of partial differential equations in one dimension is explained by relating the DG method to a particular continuous method, whose accuracy depends in part on a local analysis, and in part on information transferred from upwind elements.

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@Article{CiCP-21-905, author = {Philip Roe}, title = {A Simple Explanation of Superconvergence for Discontinuous Galerkin Solutions to $\boldsymbol{u_t}$+$\boldsymbol{u_x}$=0}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {4}, pages = {905--912}, abstract = {

The superconvergent property of the Discontinuous Galerkin (DG) method for linear hyperbolic systems of partial differential equations in one dimension is explained by relating the DG method to a particular continuous method, whose accuracy depends in part on a local analysis, and in part on information transferred from upwind elements.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0052}, url = {http://global-sci.org/intro/article_detail/cicp/11265.html} }
TY - JOUR T1 - A Simple Explanation of Superconvergence for Discontinuous Galerkin Solutions to $\boldsymbol{u_t}$+$\boldsymbol{u_x}$=0 AU - Philip Roe JO - Communications in Computational Physics VL - 4 SP - 905 EP - 912 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.OA-2016-0052 UR - https://global-sci.org/intro/article_detail/cicp/11265.html KW - AB -

The superconvergent property of the Discontinuous Galerkin (DG) method for linear hyperbolic systems of partial differential equations in one dimension is explained by relating the DG method to a particular continuous method, whose accuracy depends in part on a local analysis, and in part on information transferred from upwind elements.

Philip Roe. (2018). A Simple Explanation of Superconvergence for Discontinuous Galerkin Solutions to $\boldsymbol{u_t}$+$\boldsymbol{u_x}$=0. Communications in Computational Physics. 21 (4). 905-912. doi:10.4208/cicp.OA-2016-0052
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