Two-grid finite volume element method for linear and nonlinear elliptic problems
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Two-grid finite volume element discretization techniques, based on two linear conforming finite element spaces on one coarse and one fine grid, are presented for the two-dimensional second-order non-selfadjoint and indefinite linear elliptic problems and the two-dimensional second-order nonlinear elliptic problems. With the proposed techniques, solving the non-selfadjoint and indefinite elliptic problem on the fine space is reduced into solving a symmetric and positive definite elliptic problem on the fine space and solving the non-selfadjoint and indefinite elliptic problem on a much smaller space; solving a nonlinear elliptic problem on the fine space is reduced into solving a linear problem on the fine space and solving the nonlinear elliptic problem on a much smaller space. Convergence estimates are derived to justify the efficiency of the proposed two-grid algorithms. A set of numerical examples are presented to confirm the estimates.
Mathematics Subject Classification (2000)65N15 65N30
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- 15.Grisvard P. (1985). Elliptic Problems in Nonsmooth Domain. Pitman Advanced Pub. Program, Boston Google Scholar
- 21.Lin Q. and Zhu Q. (1994). The Preprocessing and Postprocessing for the Finite Element Methods. (in Chinese). Shanghai Scientific and Technical Publishers, Shanghai Google Scholar