Lie symmetry preserving finite element methods

Through the mathematical construction of finite element methods, the “standard” finite element method will often preserve the underlying symmetry of a given differential equation. However, this is not always the case, and while historically much attention has been paid to the preserving of conserved quantities the preservation of Lie symmetries is an open problem. We introduce a methodology for the design of arbitrary order finite element methods which preserve the underlying Lie symmetries through an equivariant moving frames based invariantization procedure.