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Digitale Medien

Finite Volume Element Approximations of Nonlocal in Time One-Dimensional Flows in Porous Media (2000)

Ewing, R. E. ; Lazarov, R. D. ; Lin, Y.

Springer

Computing 64 (2000), S. 157-182

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ISSN: 1436-5057

Schlagwort(e): AMS Subject Classifications: 65M12, 65M60, 65N40. ; Key Words: Finite volume method, parabolic equation, integro-differential equation.

Quelle: Springer Online Journal Archives 1860-2000

Thema: Informatik

Notizen: Abstract Various finite volume element schemes for parabolic integro-differential equations in 1-D are derived and studied. These types of equations arise in modeling reactive flows or material with memory effects. Our main goal is to develop a general framework for obtaining finite volume element approximations and to study the error analysis. We consider the lowest-order (linear and L-splines) finite volume elements, although higher-order volume elements can be considered as well under this framework. It is proved that finite volume element approximations are convergent with optimal order in H 1-norms, suboptimal order in the L 2-norm and super-convergent order in a discrete H 1-norm.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/s006070050007

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Digitale Medien

Local refinement techniques for elliptic problems on cell-centered grids; II. Optimal order two-grid iterative methods (1994)

Ewing, R. E. ; Lazarov, R. D. ; Vassilevski, P. S.

New York, NY [u.a.] : Wiley-Blackwell

Numerical Linear Algebra with Applications 1 (1994), S. 337-368

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ISSN: 1070-5325

Schlagwort(e): Local refinement ; Preconditioning ; Two-grid method ; Cell-centered grids ; Finite differences ; Elliptic problem ; Optimal rate of convergence ; Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik

Notizen: Two preconditioning techniques for solving difference equations arising in finite difference approximation of elliptic problems on cell-centered grids are studied. It is proven that the BEPS and the FAC preconditioners are spectrally equivalent to the corresponding finite difference schemes, including a nonsymmetric one, which is of higher-order accuracy. Numerical experiments that demonstrate the fast convergence of the preconditioned iterative methods (CG and GCG-LS in the nonsymmetric case) are presented.

Zusätzliches Material: 3 Ill.