Compactness Properties of the DG and CG Time Stepping Schemes for Parabolic Equations
Noel J. Walkington · SIAM Journal on Numerical Analysis · 2010
For a broad class of parabolic equations it is shown 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.