Numerische Mathematik

, Volume 108, Issue 2, pp 177–198 | Cite as

Two-grid finite volume element method for linear and nonlinear elliptic problems

Article

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.

Mathematics Subject Classification (2000)

65N15 65N30 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsYantai UniversityShandongPeople’s Republic of China
  2. 2.Department of MathematicsColorado State UniversityFort CollinsUSA

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