Energy-minimizing, symmetric discretizations for anisotropic meshes and energy functional extrapolation
Kühn MJ, Kruse C, Rüde U (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 43
Pages Range: A2448-A2473
Journal Issue: 4
DOI: 10.1137/21M1397520
Abstract
Self-adjoint differential operators often arise from variational calculus on energy functionals. In this case, a direct discretization of the energy functional induces a discretization of the differential operator. Following this approach, the discrete equations are naturally symmetric if the energy functional is self-adjoint, a property that may be lost when using standard difference formulas on nonuniform meshes or when the differential operator has varying coefficients. Low order finite difference or finite element systems can be derived by this approach in a systematic way and on logically structured meshes they become compact difference formulas. Extrapolation formulas used on the discrete energy can then lead to higher oder approximations of the differential operator. A rigorous analysis is presented for extrapolation used in combination with nonstandard integration rules for finite elements. Extrapolation can likewise be applied on matrix-free finite difference stencils. In our applications, both schemes show up to quartic order of convergence.
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APA:
Kühn, M.J., Kruse, C., & Rüde, U. (2021). Energy-minimizing, symmetric discretizations for anisotropic meshes and energy functional extrapolation. SIAM Journal on Scientific Computing, 43(4), A2448-A2473. https://doi.org/10.1137/21M1397520
MLA:
Kühn, Martin Joachim, Carola Kruse, and Ulrich Rüde. "Energy-minimizing, symmetric discretizations for anisotropic meshes and energy functional extrapolation." SIAM Journal on Scientific Computing 43.4 (2021): A2448-A2473.
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