MINRES for Second-Order PDEs with Singular Data
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Date
2022
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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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Keywords
Minimum residual method, Least-squares method, Discontinuous Petrov-Galerkin method, Singular data, Minimum residual method, Least-squares method, Discontinuous Petrov-Galerkin method, Singular data