Affiliation:
1. Facultad de Matemáticas , Pontificia Universidad Católica de Chile , Santiago , Chile
Abstract
Abstract
We study variants of the mixed finite element method (mixed FEM) and the first-order system least-squares finite element (FOSLS) for the Poisson problem where we replace the load by a suitable regularization which permits to use
H
−
1
H^{-1}
loads.
We prove that any bounded
H
−
1
H^{-1}
projector onto piecewise constants can be used to define the regularization and yields quasi-optimality of the lowest-order mixed FEM resp. FOSLS in weaker norms.
Examples for the construction of such projectors are given.
One is based on the adjoint of a weighted Clément quasi-interpolator.
We prove that this Clément operator has second-order approximation properties.
For the modified mixed method, we show optimal convergence rates of a postprocessed solution under minimal regularity assumptions—a result not valid for the lowest-order mixed FEM without regularization.
Numerical examples conclude this work.
Funder
Fondo Nacional de Desarrollo Científico y Tecnológico
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis
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f
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L
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