On the explicit-implicit domain decomposition method without overlapping for parabolic problems

The paper deals with studying the domain decomposition algorithm on two subdomains, where for one of them, which contains sufficiently small number of nodes, is used explicit scheme with small time step, and for another subdomain may be used effective direct algorithm (for example, subdomain is parallelepiped). This method is based on the splitting method. The algorithm formulation is given in projection form with the finite element approximation. The lumping operators technique is used for this purpose.