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 |
|---|---|
| Pages (from-to) | 1097-1115 |
| Number of pages | 19 |
| Journal | Numerische Mathematik |
| Volume | 136 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2017 Aug 1 |
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All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics
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Convergence of natural adaptive least squares finite element methods. / Carstensen, Carsten; Park, Eun Jae; Bringmann, Philipp.
In: Numerische Mathematik, Vol. 136, No. 4, 01.08.2017, p. 1097-1115.Research output: Contribution to journal › Article
TY - JOUR
T1 - Convergence of natural adaptive least squares finite element methods
AU - Carstensen, Carsten
AU - Park, Eun Jae
AU - Bringmann, Philipp
PY - 2017/8/1
Y1 - 2017/8/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85013662049&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85013662049&partnerID=8YFLogxK
U2 - 10.1007/s00211-017-0866-x
DO - 10.1007/s00211-017-0866-x
M3 - Article
VL - 136
SP - 1097
EP - 1115
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 4
ER -