A posteriori error analysis for stabilised finite element approximations of transport problems
A posteriori error analysis of finite element approximations to linear transport problems via duality arguments is considered. It is shown that the formal dual finite element approximation is not adequate. The analysis is elucidated first for the one dimensional problem in order to lead the reader to the essential points. In the center is the estimator based on the transposition of the bilinear form for the stabilized finite element method in the multidimensional case. The paper concludes with numerical examples which show that the new approach leads to sharper a posteriori error bounds and to more economical local mesh refinements.
scientific article; zbMATH DE number 1568553