Parallel characteristic finite element method for time-dependent convection-diffusion problem. (Q2918583)

The authors offer a new parallel algorithm for solving convection-dominated diffusion problems using the method of characteristics and the finite element method. The proposed algorithm is parallelized by the Schwarz overlapping domain decomposition method with parallel subspace correction (PSC). They analyze convergence of the resulting algorithm and the dependence of the convergence rate on the discretization step, time step, number of subdomains, and subdomains overlapping degree. Achieved theoretical results suggest that only one or two iterations of PSC method are needed to reach to optimal accuracy at each time level if we have a lower bound on subdomains overlapping degree independent of the discretization step and the time step. By the optimal accuracy the authors mean the error accuracy of the pure characteristic finite element method.NEWLINENEWLINEThe theoretical results are verified numerically only on a simple one-dimensional convection-diffusion problem with homogeneous Dirichlet boundary conditions. Moreover, all computations are carried out only sequentially. Therefore it is not clear from these simplified experiments how it works on real engineering problems.