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# An Adaptive Characteristic Petrov-Galerkin Finite Element Method for Convection-Dominated Linear and Nonlinear Parabolic Problems in One Space Variable

@inproceedings{Demkowicz2006AnAC, title={An Adaptive Characteristic Petrov-Galerkin Finite Element Method for Convection-Dominated Linear and Nonlinear Parabolic Problems in One Space Variable}, author={Leszek Demkowicz}, year={2006} }

- Published 2006

A new adaptive finite element method for convection-dominated problems is presented. A special feature of the method is that it is based on a Petrov-Galerkin scheme for spatial approximation at a typical time-step which employs test functions chosen so that the approximate solution coincides with the exact solution at the nodes of finite element grid. This procedure makes possible the derivation of /rul,l' local a posteriori error estimates and a very elTcctive solver. Numerical examples are… CONTINUE READING