@Article{CiCP-34-456,
author = {Blanc , XavierHermeline , FrancoisLabourasse , Emmanuel and Patela , Julie},
title = {Monotonic Diamond and DDFV Type Finite-Volume Schemes for 2D Elliptic Problems},
journal = {Communications in Computational Physics},
year = {2023},
volume = {34},
number = {2},
pages = {456--502},
abstract = {<p style="text-align: justify;">The DDFV (Discrete Duality Finite Volume) method is a finite volume scheme
mainly dedicated to diffusion problems, with some outstanding properties. This scheme
has been found to be one of the most accurate finite volume methods for diffusion
problems. In the present paper, we propose a new monotonic extension of DDFV,
which can handle discontinuous tensorial diffusion coefficient. Moreover, we compare its performance to a diamond type method with an original interpolation method
relying on polynomial reconstructions. Monotonicity is achieved by adapting the
method of Gao et al [A finite volume element scheme with a monotonicity correction
for anisotropic diffusion problems on general quadrilateral meshes] to our schemes.
Such a technique does not require the positiveness of the secondary unknowns. We
show that the two new methods are second-order accurate and are indeed monotonic
on some challenging benchmarks as a Fokker-Planck problem.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0081},
url = {http://global-sci.org/intro/article_detail/cicp/21975.html}
}