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Symmetry-Preserving Finite Element Methods: Preliminary Results

Banff International Research Station for Mathematical Innovation and Discovery

Given a differential equation that admits a group of symmetries, it is frequently desirable to preserve those symmetries when constructing a numerical scheme. For solutions that exhibit sharp variations or singularities, symmetry-preserving numerical schemes have proven to give very good numerical results. In the last 25 years, most of the research in this field has focused on the construction of symmetry-preserving finite difference numerical schemes. Extending known results to other types of numerical methods (such as finite element, finite volume, or spectral methods) remains a challenge. In this talk, I will report on preliminary results related to the construction of symmetry-preserving finite element numerical schemes. This is a joint work with Professor Alexander Bihlo from Memorial University.

Mathematics; Numerical analysis

video/mp4

Author affiliation: State University of New York New Paltz

2017-12-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63883

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/