Abstract
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.
Original language | English |
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Pages (from-to) | 1097-1115 |
Number of pages | 19 |
Journal | Numerische Mathematik |
Volume | 136 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2017 Aug 1 |
Bibliographical note
Publisher Copyright:© 2017, Springer-Verlag Berlin Heidelberg.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics