论文部分内容阅读
有限元后处理超收敛计算的EEP(单元能量投影)法以及基于该法的自适应有限元分析已在一维变分不等式问题的求解中取得显著成功。以此为基础,该文对二维变分不等式问题成功地实现了自适应有限元分析。该文提出二维区域二分法和二维C检验技术,有效地提升了松弛迭代的收敛速率,进而应用EEP超收敛公式计算超收敛解答,用其检验误差并指导网格细分。该文给出的典型数值算例表明该文算法高效、稳定、精确,解答可逐点以最大模度量满足精度要求,堪称为数值精确解。
Finite Element Finite Element Method (EEP), which is based on superconvergence calculation of Finite Element Finite Element Method (FEA) and adaptive finite element analysis based on this method, have achieved remarkable success in solving the one-dimensional variational inequality problem. Based on this, adaptive finite element analysis is successfully implemented for the two-dimensional variational inequality problem. In this paper, two-dimensional region dichotomy and two-dimensional C-test technique are proposed to effectively improve the convergence rate of relaxation iteration, and then the super convergence solution is used to calculate the super convergence solution, which is used to test the error and guide the mesh subdivision. The numerical examples given in this paper show that the proposed algorithm is efficient, stable and accurate. The solution can meet the accuracy requirements point-by-point with the maximum modulus, which is called numerical exact solution.