Quasi-Optimal Convergence Rate of an Adaptive Weakly Over-Penalized Interior Penalty Method

被引：5
|
作者：
Owens, Luke [1 ]
机构：
[1] Automated Trading Desk, Mt Pleasant, SC 29464 USA
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2014年 / 59卷 / 02期
关键词：
Discontinuous Galerkin; A posteriori error estimator; Symmetric interior penalty method; Weak over-penalization; Adaptive algorithm; Quasi-optimal convergence; FINITE-ELEMENT-METHOD;
D O I：
10.1007/s10915-013-9765-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We analyze an adaptive discontinuous finite element method (ADFEM) for the weakly over-penalized symmetric interior penalty (WOPSIP) operator applied to symmetric positive definite second order elliptic boundary value problems. For first degree polynomials, we prove that the ADFEM is a contraction for the sum of the energy error and the scaled error estimator between two consecutive loops of the adaptive algorithm. After establishing this geometric decay, we define a suitable approximation class and prove that the adaptive WOPSIP method obeys a quasi-optimal rate of convergence.
引用
收藏
页码：309 / 333
页数：25
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