Abstract
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 R 2 . 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 ∞ ( L 2 ) -norm. The interface is assumed to be of arbitrary shape but is of class C 2 for our purpose. Numerical results are presented to validate the derived estimators.
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