Construction of TVD-like Artificial Viscosities on Two-Dimensional Arbitrary FEM Grids

Quasi-second-order accurate oscillation-free schemes for the Euler equations are constructed by adjunction of an artificial viscosity term, with a coefficient determined according to symmetric TVD theory, to a two-step FEM/finite volume Richtmyer-Galerkin scheme on arbitrary (unstructured) FEM grids. Numerical experiments involving transonic and supersonic compressible flows are presented.