A discontinuous least-squares finite-element method for second-order elliptic equations |
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Authors: | Xiu Ye |
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Affiliation: | Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, USA |
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Abstract: | In this paper, a discontinuous least-squares (DLS) finite-element method is introduced. The novelty of this work is twofold, to develop a DLS formulation that works for general polytopal meshes and to provide rigorous error analysis for it. This new method provides accurate approximations for both the primal and the flux variables. We obtain optimal-order error estimates for both the primal and the flux variables. Numerical examples are tested for polynomials up to degree 4 on non-triangular meshes, i.e. on rectangular and hexagonal meshes. |
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Keywords: | Discontinuous Galerkin finite-element methods least-squares finite-element methods second-order elliptic problems polygonal mesh |
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