自适应间断Galerkin 有限元的多水平方法

本文讨论在自适应网格上间断Galerkin 有限元离散系统的局部多水平算法. 对于光滑系数和间断系数情形, 利用Schwarz 理论分析了算法的收敛性. 理论和数值试验均说明算法的收敛率与网格层数以及网格尺寸无关. 对强间断系数情形算法是拟最优的, 即收敛率仅与网格层数有关.

Local multilevel methods for adaptive discontinuous Galerkin finite element methods

In this paper, the local multilevel methods for discontinuous Galerkin finite element on adaptively refined meshes are considered. By the abstract Schwarz theory, we analyze the convergence rate of the proposed algorithms for smooth and highly discontinuous coefficients separately. It is shown that in the case of smooth coefficients, the convergence rate of the local multilevel methods is independent of mesh sizes and mesh levels. If the coefficients have large jumps, the algorithms are sub-optimal, i.e., the convergence rate is only dependent on mesh levels.