## Advances in Differential Equations

### Error estimate for approximate solutions of a nonlinear convection-diffusion problem

#### Abstract

This paper proves the estimate $\Vert{{u_\varepsilon}} - u \Vert_{L^1(Q_T)} \le C \varepsilon^{1/5}$, where, for all $\varepsilon>0$, ${{u_\varepsilon}}$ is the weak solution of $({{u_\varepsilon}})_t + {\hbox{div}} ({{\bf q}} \ f({{u_\varepsilon}}))- {\Delta}(\varphi({{u_\varepsilon}})+\varepsilon {{u_\varepsilon}}) = 0$ with initial and boundary conditions, $u$ is the entropy weak solution of $u_t + {\hbox{div}} ({{\bf q}} f(u))- {\Delta}(\varphi(u)) = 0$ with the same initial and boundary conditions, and $C>0$ does not depend on $\varepsilon$. The domain $\Omega$ is assumed to be regular and $T$ is a given positive value.

#### Article information

Source
Adv. Differential Equations Volume 7, Number 4 (2002), 419-440.

Dates
First available in Project Euclid: 27 December 2012

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