An L2-stability analysis of a θ-scheme for a class of nonlinear parabolic variational inequalities of obstacle type

This paper analyzes the stability of a fully discrete finite element approximation for a class of nonlinear parabolic variational inequalities of obstacle type. The temporal discretization is based on a θ-scheme. We derive a stability condition for the scheme that depends critically on the parameter θ. We prove that the method is unconditionally stable in the L2-norm for θ in [1/2,1]. For θ in [0,1/2), we establish a precise Courant-Friedrichs-Lewy (CFL)-type condition, Delta t