daptive Hybridized Interior Penalty Discontinuous Galerkin Methods for H(curl)-Elliptic Problems

作     者：C.Carstensen R.H.W.Hoppe N.Sharma T.Warburton 

作者机构：Department of MathematicsHumboldt Universität zu BerlinD-10099 BerlinGermany Department of Computer Science EngineeringYonsei UniversitySeoul 120-749Korea Department of MathematicsUniversity of HoustonHouston TX 77204-3008USA Institute of MathematicsUniversity of AugsburgD-86159 AugsburgGermany CAAMRice UniversityHoustonTX 77005-1892USA. 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2011年第4卷第1期

页      面：13-37页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The work of the first author has been supported by the German Na-tional Science Foundation DFG within the Research Center MATHEON and by the WCU program through KOSEF(R31-2008-000-10049-0).The other authors acknowledge sup-port by the NSF grant DMS-0810176.1 

主　　题：Adaptive hybridized Interior Penalty Discontinuous Galerkin method a posteriori error analysis H(curl)-elliptic boundary value problems semi-discrete eddy currents equations 

摘      要：We develop and analyze an adaptive hybridized Interior Penalty Discontinuous Galerkin(IPDG-H)method for H(curl)-elliptic boundary value problems in 2D or 3D arising from a semi-discretization of the eddy currents *** method can be derived from a mixed formulation of the given boundary value problem and involves a Lagrange multiplier that is an approximation of the tangential traces of the primal variable on the interfaces of the underlying triangulation of the computational *** is shown that the IPDG-H technique can be equivalently formulated and thus implemented as a mortar *** mesh adaptation is based on a residual-type a posteriori error estimator consisting of element and face *** a unified framework for adaptive finite element methods,we prove the reliability of the estimator up to a consistency *** performance of the adaptive symmetric IPDG-H method is documented by numerical results for representative test examples in 2D.