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Journal of Scientific Computing

, Volume 64, Issue 1, pp 130–150 | Cite as

Adaptive Bilinear Element Finite Volume Methods for Second-Order Elliptic Problems on Nonmatching Grids

  • Yanli Chen
  • Yonghai Li
  • Zhiqiang Sheng
  • Guangwei Yuan
Article
  • 201 Downloads

Abstract

In this article, we propose and analyze two kinds of adaptive bilinear element finite volume methods for second-order elliptic problems on nonmatching grids. One of them chooses the piecewise bilinear finite element space as the trial function space, which is continuous on the matching part of a grid and is discontinuous on the nonmatching part of it. The other directly uses discontinuous piecewise bilinear element space for the trial function space. A priori estimations ensure the convergence and a posteriori estimations pave the way for adaptive methods. Several numerical experiments are presented to conform our theoretical results.

Keywords

Finite volume method Discontinuous Galerkin method  A posteriori estimates Hanging nodes Elliptic problems 

Mathematics Subject Classification

65N08 65N15 65N30 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yanli Chen
    • 1
  • Yonghai Li
    • 2
  • Zhiqiang Sheng
    • 3
  • Guangwei Yuan
    • 3
  1. 1.Institute of MathematicsJilin UniversityChangchunPeople’s Republic of China
  2. 2.School of MathematicsJilin UniversityChangchunPeople’s Republic of China
  3. 3.Laboratory of Science and Technology on Computational PhysicsInstitute of Applied Physics and Computational MathematicsBeijingPeople’s Republic of China

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