A posteriori error analysis of the Crank-Nicolson finite element method for linear parabolic interface problems: A reconstruction approach

This article studies a residual-based a posteriori error analysis for the Crank-Nicolson time-stepping finite element method for a linear parabolic interface problem in a bounded convex polygonal domain in R2. A piecewise linear finite element space is used in space that is allowed to change in time and a modified Crank-Nicolson approximation is applied for the time discretizations. We employ a space-time reconstruction that is piecewise quadratic in time and the Clément-type interpolation estimates to derive optimal order in time and an almost optimal order in space a posteriori error bound in the L∞(L2)-norm. The interface is assumed to be of arbitrary shape but is of class C2 for our purpose. Numerical results are presented to validate the derived estimators.