Second order monotone finite differences discretization of linear anisotropic differential operators
J. Frédéric Bonnans, Guillaume Bonnet, Jean-Marie Mirebeau
Source 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 dimensions two and three. Numerical experiments illustrate the efficiency of our method in several contexts.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.