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  • Research Article
  • Open Access

Convergence of a Mimetic Finite Difference Method for Static Diffusion Equation

  • 1Email author,
  • 2,
  • 3 and
  • 4
Advances in Difference Equations20072007:012303

  • Received: 23 January 2007
  • Accepted: 19 April 2007
  • Published:


The numerical solution of partial differential equations with finite differences mimetic methods that satisfy properties of the continuum differential operators and mimic discrete versions of appropriate integral identities is more likely to produce better approximations. Recently, one of the authors developed a systematic approach to obtain mimetic finite difference discretizations for divergence and gradient operators, which achieves the same order of accuracy on the boundary and inner grid points. This paper uses the second-order version of those operators to develop a new mimetic finite difference method for the steady-state diffusion equation. A complete theoretical and numerical analysis of this new method is presented, including an original and nonstandard proof of the quadratic convergence rate of this new method. The numerical results agree in all cases with our theoretical analysis, providing strong evidence that the new method is a better choice than the standard finite difference method.


  • Diffusion Equation
  • Discrete Version
  • Finite Difference Method
  • Static Diffusion
  • Integral Identity


Authors’ Affiliations

Departamento de Matemáticas, Universidad Central de Venezuela, Apdo. 6228, Carmelitas, Caracas, 1010, Venezuela
Departamento de Física, Universidad Simón Bolívar, Ofic. 220, Sartenejas, Baruta, Edo., Miranda Coding Postal 1082, Venezuela
Departamento de Matemática y Física, Universidad Pedagógica Experimental Libertador, Avenida Páez, El Paraiso, Caracas Coding Postal 1020, Venezuela
Computational Science Research Center, San Diego State University, 5500 Campanile Dr.,, San Diego, CA 92182-1245, USA


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© J. M. Guevara-Jordan et al. 2007

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