Convergence analysis of an adaptive nonconforming finite element method

被引:9
作者
Carstensen, C
Hoppe, RHW
机构
[1] Humboldt Univ, Dept Math, D-10099 Berlin, Germany
[2] Univ Augsburg, Inst Math, D-86159 Augsburg, Germany
[3] Univ Houston, Dept Math, Houston, TX 77204 USA
关键词
Finite Element Method; Lower Order; Convergence Analysis; Refinement Process; Data Control;
D O I
10.1007/s00211-005-0658-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
An adaptive nonconforming finite element method is developed and analyzed that provides an error reduction due to the refinement process and thus guarantees convergence of the nonconforming finite element approximations. The analysis is carried out for the lowest order Crouzeix-Raviart elements and leads to the linear convergence of an appropriate adaptive nonconforming finite element algorithm with respect to the number of refinement levels. Important tools in the convergence proof are a discrete local efficiency and a quasi-orthogonality property. The proof does neither require regularity of the solution nor uses duality arguments. As a consequence on the data control, no particular mesh design has to be monitored.
引用
收藏
页码:251 / 266
页数:16
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