UNIFIED ERROR ANALYSIS OF DISCONTINUOUS GALERKIN METHODS FOR PARABOLIC OBSTACLE PROBLEM

We introduce and study various discontinuous Galerkin (DG) finite element approximations for a parabolic variational inequality associated with a general obstacle problem in Double-struck capital R-d (d = 2, 3). For the fully-discrete DG scheme, we employ a piecewise linear finite element space for spatial discretization, whereas the time discretization is carried out with the implicit backward Euler method. We present a unified error analysis for all well known symmetric and non-symmetric DG fully discrete schemes, and derive error estimate of optimal order O(h + Delta t) in an energy norm. Moreover, the analysis is performed without any assumptions on the speed of propagation of the free boundary and only the realistic regularity u(t) is an element of L-2(0, T; L-2(Omega)) is assumed. Further, we present some numerical experiments to illustrate the performance of the proposed methods.