<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The major emphasis of this work is the derivation of a posteriori error estimates for the mixed finite volume discretization of second-order elliptic equations. The estimates are established for meshes consisting of simplices on unstructured grids. We consider diffusion problems with nonhomogeneous diffusion coefficients. The error estimates are of residual types and are formulated in the energy semi-norm for a locally postprocessed approximate solutions. The estimates are fully computable and locally efficient that they can serve as indicators for adaptive refinement and for the actual control of the error. Numerical results are shown for two test examples in two space dimensions. It is found that the proposed adaptive mixed finite volume method offers a robust and accurate approach for solving second-order elliptic equations, even when highly nonhomogeneous diffusion coefficients are used in the simulations.</p></abstract>

The major emphasis of this work is the derivation of a posteriori error estimates for the mixed finite volume discretization of second-order elliptic equations. The estimates are established for meshes consisting of simplices on unstructured grids. We consider diffusion problems with nonhomogeneous diffusion coefficients. The error estimates are of residual types and are formulated in the energy semi-norm for a locally postprocessed approximate solutions. The estimates are fully computable and locally efficient that they can serve as indicators for adaptive refinement and for the actual control of the error. Numerical results are shown for two test examples in two space dimensions. It is found that the proposed adaptive mixed finite volume method offers a robust and accurate approach for solving second-order elliptic equations, even when highly nonhomogeneous diffusion coefficients are used in the simulations.

A posteriori error estimates for mixed finite volume solution of elliptic boundary value problems

Université Paris 13, Sorbonne Paris Cité

Laboratory of Complex Systems Engineering & Human Systems

School of Engineering and Computing Sciences

Université des sciences, des techniques et des technologies de Bamako

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The major emphasis of this work is the derivation of a posteriori error estimates for the mixed finite volume discretization of second-order elliptic...

A posteriori error estimates for mixed finite volume solution of elliptic boundary value problems

Published Online: Jul 28, 2018

Page range: 199 - 217

Received: Jun 01, 2018

Accepted: Jun 25, 2018

DOI: https://doi.org/10.1515/mjpaa-2017-0016

Keywords
A posteriori error estimate, mixed finite volume methods, second-order elliptic equations, unstructured mesh, diffusion equations

© 2018 Fayssal Benkhaldoun et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A posteriori error estimates for mixed finite volume solution of elliptic boundary value problems

Published Online: Jul 28, 2018

Page range: 199 - 217

Received: Jun 01, 2018

Accepted: Jun 25, 2018

DOI: https://doi.org/10.1515/mjpaa-2017-0016

KeywordsA posteriori error estimate, mixed finite volume methods, second-order elliptic equations, unstructured mesh, diffusion equations

© 2018 Fayssal Benkhaldoun et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
A posteriori error estimate, mixed finite volume methods, second-order elliptic equations, unstructured mesh, diffusion equations