An exponential Integrator for finite volume discretization of nonlinear parabolic differential equation
Numerical Analysis
2015-08-20 v2
Abstract
We consider the numerical approximation of a general second order semi--linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media which is fundamental in many geo-engineering applications, including oil and gas recovery from subsurface. Using the finite volume with two-point flux approximation on regular mesh combined with exponential time differencing of order one (ETD1) for temporal discretization, we derive the estimate under the assumption that the non linear term is locally Lipschitz. Numerical simulations to sustain the theoretical results are provided.
Keywords
Cite
@article{arxiv.1209.1828,
title = {An exponential Integrator for finite volume discretization of nonlinear parabolic differential equation},
author = {Antoine Tambue},
journal= {arXiv preprint arXiv:1209.1828},
year = {2015}
}