$L^1$--Framework for
Continuous Dependence and Error Estimates
for Quasilinear Anisotropic Degenerate Parabolic Equations
Author: Gui-Qiang Chen and Kenneth Karlsen
Title:
$L^1$--Framework for
Continuous Dependence and Error Estimates
for Quasilinear Anisotropic Degenerate Parabolic Equations
Abstract
We develop a general $L^1$--framework for deriving
continuous dependence and
error estimates for quasilinear anisotropic degenerate parabolic
equations with the aid of the Chen-Perthame kinetic
approach.
We apply our $L^1$--framework to establish
an explicit estimate for continuous dependence on the nonlinearities
and an optimal error estimate for the vanishing anisotropic viscosity
method, without imposition of bounded variation of the approximate
solutions. Finally, as an example of a direct application of this framework
to numerical methods, we focus on a linear convection-diffusion
model equation and derive an $L^1$ error estimate
for an upwind-central finite difference scheme.
This article has appeared in:
Transactions of the American Mathematical Society (TAMS)
, Vol. ?? , page ?? (2004).
This paper is available in the following formats:
A closely related paper is Change me.
Author Address
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
gqchen@math.nwu.edu