Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Second order monotone finite differences discretization of linear anisotropic differential operators

Abstract : We design adaptive finite differences discretizations, which are degenerate elliptic and second order consistent, of linear and quasi-linear partial differential operators featuring both a first order term and an anisotropic second order term. Our approach requires the domain to be discretized on a Cartesian grid, and takes advantage of techniques from the field of low-dimensional lattice geometry. We prove that the stencil of our numerical scheme is optimally compact, in dimension two, and that our approach is quasi-optimal in terms of the compatibility condition required of the first and second order operators, in dimension two and three. Numerical experiments illustrate the efficiency of our method in several contexts.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03084046
Contributor : Guillaume Bonnet <>
Submitted on : Monday, March 8, 2021 - 2:16:46 PM
Last modification on : Friday, April 30, 2021 - 9:58:30 AM

File

AnisotropicFirstOrder.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03084046, version 2

Citation

Frédéric Bonnans, Guillaume Bonnet, Jean-Marie Mirebeau. Second order monotone finite differences discretization of linear anisotropic differential operators. 2021. ⟨hal-03084046v2⟩

Share

Metrics

Record views

46

Files downloads

21