Voronin K.   Laevsky Y.  

Numerical study of application of flux splitting schemes in case of non-uniform meshes

Reporter: Voronin K.

In this work behavior of flux splitting schemes in mixed FEM for heat transfer problems is considered in the case of non-uniform meshes. Flux splitting schemes are constructed by an approach which is based on using scalar splitting scheme for heat flux divergence. A priori stability estimates for initial data in the subspace of discrete Hdiv space were obtained in [1] for flux splitting schemes in two- and three-dimensional cases. In the a priori estimates the initial heat flux is required to possess additional smoothness. In general case, however, this assumption is not valid [2]. The main attention in the paper is focused on numerical study of the arising conditional convergence issues and development of efficient ways which allow one to increase smoothness of initial heat flux and can be used in solving application problems.
The project has been partially supported by grants No. 15-11-10024 of Russian Science Foundation.

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