Analysis of a discontinuous Galerkin pressure correction scheme for the Kelvin-Voigt equation

Abstract

We formulate and analyze a discontinuous Galerkin pressure correction scheme for solving the Kelvin-Voigt. The proposed scheme is proven to be unconditionally stable. Convergence of the discrete velocity is established through a priori error estimates in $L^2$ and $DG$ norms, and validating our findings through numerical experiments. The theoretical analysis confirms optimal convergence rates in the $DG$ norm, and optimal spatial accuracy in the $L^2$ norm, though temporal accuracy appears suboptimal. Nevertheless, numerical experiments indicate that the scheme achieves optimal accuracy in both time and space.