Symmetry-preserving finite element schemes: An introductory investigation

Alexander Bihlo; Francis Valiquette

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arXiv · 1803.10058

Symmetry-preserving finite element schemes: An introductory investigation

Alexander Bihlo·Francis Valiquette

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Abstract

Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our constructions can be extended to (1+1)-dimensional evolutionary partial differential equations, using Burgers' equation as an example. Numerical simulations verify that the symmetry-preserving finite element schemes constructed converge at the expected rate and that these schemes can yield better results than their non-invariant finite element counterparts.

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Alexander Bihlo, Francis Valiquette. 2018-03-27. Symmetry-preserving finite element schemes: An introductory investigation. https://arxiv.org/abs/1803.10058

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