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Two-grid methods for finite volume element approximations of nonlinear parabolic equations

✍ Scribed by Chuanjun Chen; Min Yang; Chunjia Bi

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
633 KB
Volume
228
Category
Article
ISSN
0377-0427

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✦ Synopsis

a b s t r a c t Two-grid methods are studied for solving a two dimensional nonlinear parabolic equation using finite volume element method. The methods are based on one coarse-grid space and one fine-grid space. The nonsymmetric and nonlinear iterations are only executed on the coarse grid and the fine-grid solution can be obtained in a single symmetric and linear step. It is proved that the coarse grid can be much coarser than the fine grid. The two-grid methods achieve asymptotically optimal approximation as long as the mesh sizes satisfy

| ln H|). As a result, solving such a large class of nonlinear parabolic equations will not be much more difficult than solving one single linearized equation.

πŸ“œ SIMILAR VOLUMES

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✍ Chuanjun Chen; Wei Liu πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 632 KB

## a b s t r a c t The two-grid method is studied for solving a two-dimensional second-order nonlinear hyperbolic equation using finite volume element method. The method is based on two different finite element spaces defined on one coarse grid with grid size H and one fine grid with grid size h, r

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