artículo
MINRES for Second-Order PDEs with Singular Data
Date
2022Registration in:
10.1137/21M1457023
1095-7170
0036-1429
WOS:000814569400005
Author
Führer Thomas
Heuer, Norbert
Karkulik, Michael
Institutions
Abstract
Minimum residual methods such as the least-squares finite element method (FEM) or the discontinuous Petrov-Galerkin (DPG) method with optimal test functions usually exclude singular data, e.g., non-square-integrable loads. We consider a DPG method and a least-squares FEM for the Poisson problem. For both methods we analyze regularization approaches that allow the use of H-1 loads and also study the case of point loads. For all cases we prove appropriate convergence orders. We present various numerical experiments that confirm our theoretical results. Our approach extends to general well-posed second-order problems.
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