A posteriori analysis and adaptive error control for operator decomposition solution of coupled semilinear elliptic systems

作者：Carey V; Estep D^*; Tavener S

来源：International Journal for Numerical Methods in Engineering, 2013, 94(9): 826-849.

DOI：10.1002/nme.4482

• a posteriori error estimates
• adjoint problem
• dual problem
• error estimates
• finite element method
• generalized Green's function
• operator splitting
• operator decomposition
• coupled problems

In this paper, we develop an a posteriori error analysis for operator decomposition iteration methods applied to systems of coupled semilinear elliptic problems. The goal is to compute accurate error estimates that account for the combined effects arising from numerical approximation (discretization) and operator decomposition iteration. In an earlier paper, we considered triangular' systems that can be solved without iteration. In contrast, operator decomposition iterative methods for fully coupled systems involve an iterative solution technique. We construct an error estimate for the numerical approximation error that specifically addresses the propagation of error between iterates and provide a computable estimate for the iteration error arising because of the decomposition of the operator. Finally, we develop an adaptive discretization strategy to systematically reduce the discretization error.

• 出版日期2013-6-1