An efficient symmetric finite volume element method for second-order variable coefficient parabolic integro-differential equations. (English) Zbl 1463.65348
Summary: This paper is devoted to develop a symmetric finite volume element (FVE) method to solve second-order variable coefficient parabolic integro-differential equations, arising in modeling of nonlocal reactive flows in porous media. Based on barycenter dual mesh, one semi-discrete and two fully discrete backward Euler and Crank-Nicolson symmetric FVE schemes are presented. Then, the optimal order error estimates in \(L^2\)-norm are derived for the semi-discrete and two fully discrete schemes. Numerical experiments are performed to examine the convergence rate and verify the effectiveness and usefulness of the new numerical schemes.
MSC:
| 65N08 | Finite volume methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35R09 | Integro-partial differential equations |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 76S05 | Flows in porous media; filtration; seepage |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
parabolic integro-differential equations; barycenter dual mesh; symmetric FVE schemes; \(L^2\)-norm error estimatesReferences:
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