On one domain decomposition method with nonmatching grids for solving parabolic equations

In the article we propose and study a noniterative domain decomposition algorithm without overlapping subdomains and with the use of the penalty functionals on the interface between subdomains. Such type of algorithms were consideredearlier. In all these works the error estimate for optimal penalty parameter is O = √τ. In this work the error estimate is improved and our approach, where the alternating direction type splitting was used.