An adaptive BDDC preconditioner for advection-diffusion problems with a stabilized finite element discretization (Q2029117)

The authors are concerned with the balancing domain decomposition by constraints (BDDC) method in order to solve accurately, i.e., to remove spurious oscillations of solutions to some 2D and 3D Dirichlet boundary value problems attached to advection-diffusion equation in a bounded Lipschitz polyhedral domain. Thus, they propose a BDDC preconditioner in order to solve the corresponding nonsymmetric and positive definite (NSPD) system generated by stabilized Galerkin/least-squares method. The coarse component required for the adaptive BDDC preconditioner is constructed and the convergence theory of the GMRES algorithm preconditioned by the adaptive BDDC method is carried out. With the aid of three numerical examples the authors underline the performances of this BDDC preconditioner with an adaptive coarse space developed for the stabilized finite element formulation of the advection-diffusion problem.