Majorizing difference schemes for parabolic equations on unstructured grids (Q1128394)

We propose a method for the numerical solution of multidimensional problems modeled by parabolic equations in domains of complex shape with several unconnected boundaries. The proposed method combines the high efficiency of finite element methods for discretization of the integration domain (unstructured grids, single-index numbering of grid nodes, etc.) with the capabilities of ordinary grid approaches (analysis of approximation, stability, etc.). The approach used for the construction of this method is similar to that previously proposed for hyperbolic and elliptic equations, and it is demonstrated in what follows in application to the simplest two-dimensional equations of heat conduction.