Convergence analysis of a symmetric dual-wind discontinuous Galerkin method for a parabolic variational inequality

This paper investigates a symmetric dual-wind discontinuous Galerkin (DG) method for solving parabolic variational inequalities. By employing a symmetric dual-wind DG discretization in space and a backward Euler discretization in time, we propose a fully discrete scheme to solve a time-dependent obstacle problem. Under reasonable regularity assumptions on the exact solution, we prove the convergence of numerical solutions with rates in the L∞(L2) and L2(H1)-like energy errors by introducing a new interpolation operator which is a combination of the standard interpolation operator and a positive-preserving interpolation operator. Numerical experiments are provided to validate the effectiveness of the proposed method.