Twogrid finite volume element method for linear and nonlinear elliptic problems
 Chunjia Bi,
 Victor Ginting
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Twogrid finite volume element discretization techniques, based on two linear conforming finite element spaces on one coarse and one fine grid, are presented for the twodimensional secondorder nonselfadjoint and indefinite linear elliptic problems and the twodimensional secondorder nonlinear elliptic problems. With the proposed techniques, solving the nonselfadjoint 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 nonselfadjoint 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 twogrid algorithms. A set of numerical examples are presented to confirm the estimates.
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 Title
 Twogrid finite volume element method for linear and nonlinear elliptic problems
 Journal

Numerische Mathematik
Volume 108, Issue 2 , pp 177198
 Cover Date
 20071201
 DOI
 10.1007/s0021100701159
 Print ISSN
 0029599X
 Online ISSN
 09453245
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 65N15
 65N30
 Industry Sectors
 Authors

 Chunjia Bi ^{(1)}
 Victor Ginting ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Yantai University, Shandong, 264005, People’s Republic of China
 2. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA