A New Approach to Constructing Splitting Schemes in Mixed FEM for Heat Transfer: A Priori Estimates
A priori estimates for a new approach to constructing vector splitting schemes in mixed FEM for heat transfer problems are presented. Heat transfer problem is considered in the mixed weak formulation approximated by Raviart-Thomas finite elements of lowest order on rectangular meshes. The main idea of the considered approach is to develop splitting schemes for the heat flux using well-known splitting scheme for the scalar function of flux divergence. Based on flux decomposition into discrete divergence-free and potential (orthogonal) components, a priori estimates for 2D and 3D vector splitting schemes are presented. Special attention is given to the additional smoothness requirements imposed on the initial heat flux. The role of these requirements is illustrated by several numerical examples.
- 1.Voronin, K.V., Laevsky Y.M.: An approach to the construction of flow splitting schemes in the mixed finite element method. Math. Mod. and Comp. Simul. (to appear)Google Scholar