Two-grid economical algorithms for parabolic integro-differential equations with nonlinear memory. (English) Zbl 1426.65185
The authors propose several two-grid finite element algorithms for solving parabolic integro-differential equations with nonlinear memory. It is obtained that these algorithms are as stable as the standard fully discrete finite element algorithm, and can achieve the same accuracy as the standard algorithm if the coarse grid size \(H\) and the fine grid size \(h\) satisfy \(H =O(h^{(r-1)/r})\).
Reviewer: Marius Ghergu (Dublin)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65D30 | Numerical integration |
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 35R09 | Integro-partial differential equations |
| 45K05 | Integro-partial differential equations |
Keywords:
parabolic integro-differential equation; two-grid method; error estimate; finite element method; stability; backward Euler schemeReferences:
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