Symmetry-preserving finite element schemes: An introductory\n investigation

2018/03/27 by Alexander Bihlo, Bihlo, Alexander, Francis Valiquette +1
Engineering · #Vibration and Dynamic Analysis

paper · pdf · doi:10.48550/arxiv.1803.10058

Abstract

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

Related

• On the development of symmetry-preserving finite element schemes for ordinary differential equations
• Symmetry-preserving numerical schemes
• Symmetry Preserving Numerical Schemes for Partial Differential Equations\n and their Numerical Tests
• Invariant Reduction for Partial Differential Equations. II: The General Mechanism
• Symmetry-preserving discrete schemes for some heat transfer equations