We describe the basic ideas needed to obtain apriori error estimates for a nonlinear convection diffusion equation discretized by higher order conforming finite elements. For simplicity of presentation, we derive the key estimates under simplified assumptions, e.g. Dirichlet-only boundary conditions. The resulting error estimate is obtained using continuous mathematical induction for the space semi-discrete scheme.
@article{702718,
title = {Error estimates for nonlinear convective problems in the finite element method},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2013},
pages = {136-141},
url = {http://dml.mathdoc.fr/item/702718}
}
Kučera, Václav. Error estimates for nonlinear convective problems in the finite element method, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2013), pp. 136-141. http://gdmltest.u-ga.fr/item/702718/