Abstract
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.
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The work is supported by the National Natural Science Foundation of China (Grant No: 10601045).
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Bi, C., Ginting, V. Two-grid finite volume element method for linear and nonlinear elliptic problems. Numer. Math. 108, 177–198 (2007). https://doi.org/10.1007/s00211-007-0115-9
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DOI: https://doi.org/10.1007/s00211-007-0115-9