A new approach to constructing vector splitting schemes in mixed finite element method for parabolic problems

Abstract

AbstractA general setting for a new approach to constructing vector splitting schemes in mixed FEM for heat transfer problem is considered. For space approximation Raviart–Thomas finite elements of lowest order are implemented on rectangular (parallelepiped) mesh. The main question discussed is how to implement time discretization so as to obtain efficient numerical algorithms.The key idea of the proposed approach is to use scalar splitting schemes for heat flux divergence. This allows one to carry out accuracy and stability analysis on the basis of the well-known results for underlying scalar splitting schemes.