Compactness Properties of the DG and CG Time Stepping Schemes for Parabolic Equations

Abstract. It is shown that for a broad class of equations that numerical solutions computed using the discontinuous Galerkin or the continuous Galerkin time stepping schemes of arbitrary order will inherit the compactness properties of the underlying equation. Convergence of numerical schemes for a phase field approximation of the flow of two fluids with surface tension is presented to illustrate these results. Key words. discontinuous Galerkin, continuous Galerkin, parabolic equations.

• Type: Journal
• Year: 2010
• Where: SIAMNUM
• Authors: Noel Walkington
• Keywords: Continuous Galerkin Time, Discontinuous Galerkin, Phase Field Approximation, SIAMNUM 2010