Convergence Analysis of Adaptive Mixed and Nonconforming Finite Element Methods

摘要：

We are concerned with a convergence analysis of adaptive mixed and nonconfoming finite element methods for second order elliptic boundary value problems. In case of standard conforming Lagrangian type finite element approximations, such an analysis has been initiated in 11 and has been further investigated in 6,14,15. The methods presented in this contribution provide a guaranteed reduction of the discretization error. The analysis is carried out for a model problem and discretizations by the lowest order Raviart-Thomas and Crouzeix-Raviart finite elements. The essential steps in the convergence proof are the reliability of the estimator, a discrete local efficiency, and quasi-orthogonality properties. We do not require any regularity of the solution nor do we make use of duality arguments.

关键词： a posteriori error estimation convergence analysis adaptive mixed finite elements adaptive nonconforming finite elements

作者: Ronald H.W. Hoppe Carsten Carstensen

作者单位: Department of Mathematics, University of Houston, Houston, TX 77204-3008 and Institute of Mathematic Department of Mathematics, Humboldt Universitat zu Berlin, D-10099 Berlin

会议类型: 国际会议

会议名称: The Fourth International Workshop on Scientific Computing and Applications(第四届国际科学计算与应用研讨会)

会议地点: 上海

会议语种:英文

页码: 38-49

在线出版日期: 2005-06-20（万方平台首次上网日期，不代表论文的发表时间）