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

作者：Sen Gupta Jhuma; Sinha Rajen Kumar^*; Reddy Gujji Murali Mohan; Jain Jinank

来源：Journal of Computational and Applied Mathematics, 2018, 340: 173-190.

DOI：10.1016/j.cam.2018.02.022

• Parabolic interface problems
• Crank-Nicolson approximation
• Elliptic reconstruction
• Clement-type interpolation estimates
• A posteriori error analysis

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 Clement-type interpolation estimates to derive optimal order in time and an almost optimal order in space a posteriori error bound in the L-infinity(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.

• 出版日期2018-10-1