A NEW APPROACH TO RECOVERY OF DISCONTINUOUS GALERKIN

作     者：Sebastian Franz Lutz Tobiska Helena Zarin 

作者机构：Institutfür Numerische MathematikTechnische Universitt Dresden Institutfür Analysis und NumerikOtto-von-Guericke Universitt Magdeburg Department of Mathematics and InformaticsUniversity of Novi SadTrg Dositeja Obradovica 421 000 Novi Sad 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2009年第27卷第6期

页      面：697-712页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the Ministry of Science and Technological Development of the Republic of Serbia  grant 144006 

主　　题：Discontinuous Galerkin Postprocessing Recovery. 

摘      要：A new recovery operator P ：Qn^disc（T）→Qn＋1^disc（M） for discontinuous Galerkin is derived. It is based on the idea of projecting a discontinuous, piecewise polynomial solution on a given mesh T into a higher order polynomial space on a macro mesh M. In order to do so, we define local degrees of freedom using polynomial moments and provide global degrees of freedom on the macro mesh. We prove consistency with respect to the local L2-projection, stability results in several norms and optimal anisotropic error estimates. As an example, we apply this new recovery technique to a stabilized solution of a singularly perturbed convection-diffusion problem using bilinear elements.