The first-order div least squares finite element methods provide inherent a posteriori error estimator by the elementwise evaluation of the functional. In this paper we prove Q-linear convergence of the associated adaptive mesh-refining strategy for a sufficiently fine initial mesh with some sufficiently large bulk parameter for piecewise constant right-hand sides in a Poisson model problem. The proof relies on some modification of known supercloseness results to non-convex polygonal domains plus the flux representation formula. The analysis is carried out for the lowest-order case in two-dimensions for the simplicity of the presentation.
Bibliographical noteFunding Information:
This research was supported by the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Reliable simulation techniques in solid mechanics. Development of non- standard discretization methods, mechanical and mathematical analysis” under the project “Foundation and application of generalized mixed FEM towards nonlinear problems in solid mechanics” (CA 151/22-1). This research was supported in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology NRF 2011-0030934 and NRF-2015R1A5A1009350.
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All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics