期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 79, 期 1, 页码 414-441出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-018-0860-1
关键词
Parabolic integro-differential equations; Finite element method; Ritz-Volterra reconstruction; Crank-Nicolson method; A posteriori error estimate
资金
- FAPESP [2016/19648-9]
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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