Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Energy-minimizing, symmetric finite differences for anisotropic meshes and energy functional extrapolation

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 was 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [24 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02941899
Contributor : Martin Joachim Kühn Connect in order to contact the contributor
Submitted on : Thursday, September 17, 2020 - 2:14:17 PM
Last modification on : Wednesday, October 14, 2020 - 3:41:58 AM
Long-term archiving on: : Thursday, December 3, 2020 - 9:40:52 AM

File

kuehn_kruse_ruede_energy_minim...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02941899, version 1

Collections

`

Citation

Martin Joachim Kühn, Carola Kruse, Ulrich Rüde. Energy-minimizing, symmetric finite differences for anisotropic meshes and energy functional extrapolation. 2020. ⟨hal-02941899⟩

Share

Metrics

Record views

117

Files downloads

120