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- Title
Ritz–Volterra reconstructions and a posteriori error analysis of finite element method for parabolic integro-differential equations.
- Authors
Reddy, G. Murali Mohan; Sinha, Rajen K.
- Abstract
We derive a posteriori error estimates for both semidiscrete and implicit fully discrete backward Euler method for linear parabolic integro-differential equations in a bounded convex polygonal or polyhedral domain. A novel space–time reconstruction operator is introduced, which is a generalization of the elliptic reconstruction operator [2003, SIAM J. Numer. Anal., 41, pp. 1585–1594], and we call it as Ritz–Volterra reconstruction operator. The Ritz–Volterra reconstruction operator in conjunction with the linear approximation of the Volterra integral term is used in a crucial way to derive optimal order a posteriori error estimates in L∞(L2) and L2(H1)-norms. The related a posteriori error estimates for the Ritz–Volterra reconstruction error are also established. We allow only nested refinement of the space meshes for the fully discrete analysis.
- Subjects
NUMERICAL analysis; MATHEMATICAL analysis; FINITE element method; DIFFERENTIAL equations
- Publication
IMA Journal of Numerical Analysis, 2015, Vol 35, Issue 1, p341
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/drt059