Invariant meshless discretization schemes

Abstract

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a way of associating invariant functions to non-invariant functions. An invariant meshless approximation of a nonlinear diffusion equation is constructed. Comparative numerical tests with a non-invariant meshless scheme are presented. These tests yield that invariant meshless schemes can lead to substantially improved numerical solutions compared to numerical solutions generated by non-invariant meshless schemes.

10 pages, 2 figures, release version

References in corpus (2)

• Invariant discretization schemes for the shallow-water equations
• Invariant Discretization Schemes Using Evolution-Projection Techniques

Cited by in corpus (3)

• Lie-point symmetries of the discrete Liouville equation
• Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests
• Invariant Discretization of Partial Differential Equations Admitting Infinite-Dimensional Symmetry Groups