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.
Citation
Robert Eymard. Thierry Gallouët. Raphaèle Herbin. "Error estimate for approximate solutions of a nonlinear convection-diffusion problem." Adv. Differential Equations 7 (4) 419 - 440, 2002. https://doi.org/10.57262/ade/1356651802
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