Abstract

We propose a family of mimetic discretization schemes for elliptic problems including convection and reaction terms. Our approach is an extension of the mimetic methodology for purely diffusive problems on unstructured polygonal and polyhedral meshes. The a priori error analysis relies on the connection between the mimetic formulation and the lowest order Raviart–Thomas mixed finite element method. The theoretical results are confirmed by numerical experiments.

MSC codes

  1. 65N06
  2. 65N12
  3. 65N15
  4. 65N22
  5. 65N30

Keywords

  1. mimetic finite difference method
  2. boundary value problem
  3. diffusion-convection-reaction equation
  4. Raviart–Thomas finite element space
  5. dual mixed formulation
  6. polyhedral mesh

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Information

Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 2612 - 2637
ISSN (online): 1095-7170

History

Submitted: 4 March 2008
Accepted: 6 March 2009
Published online: 22 July 2009

MSC codes

  1. 65N06
  2. 65N12
  3. 65N15
  4. 65N22
  5. 65N30

Keywords

  1. mimetic finite difference method
  2. boundary value problem
  3. diffusion-convection-reaction equation
  4. Raviart–Thomas finite element space
  5. dual mixed formulation
  6. polyhedral mesh

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