Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 79, Issue 1, Pages 414-441Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-018-0860-1
Keywords
Parabolic integro-differential equations; Finite element method; Ritz-Volterra reconstruction; Crank-Nicolson method; A posteriori error estimate
Categories
Funding
- FAPESP [2016/19648-9]
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We study a posteriori error analysis for the space-time discretizations of linear parabolic integro-differential equation in a bounded convex polygonal or polyhedral domain. The piecewise linear finite element spaces are used for the space discretization, whereas the time discretization is based on the Crank-Nicolson method. The Ritz-Volterra reconstruction operator (IMA J Numer Anal 35:341-371, 2015), a generalization of elliptic reconstruction operator (SIAM J Numer Anal 41:1585-1594, 2003), is used in a crucial way to obtain optimal rate of convergence in space. Moreover, a quadratic (in time) space-time reconstruction operator is introduced to establish second order convergence in time. The proposed method uses nested finite element spaces and the standard energy technique to obtain optimal order error estimator in the L-infinity(L-2)-norm. Numerical experiments are performed to validate the optimality of the error estimators.
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