BDDC Preconditioners for Divergence Free Virtual Element Discretizations of the Stokes Equations

Abstract The virtual element method (VEM) is a new family of numerical methods for the approximation partial differential equations, where geometry polytopal mesh elements can be very general. aim this article to extend balancing domain decomposition by constraints preconditioner solution saddle-point linear system arising from VEM discretization two-dimensional Stokes equations. Under suitable hypotesis on choice primal unknowns, preconditioned results symmetric and positive definite, thus conjugate gradient used its solution. We provide theoretical convergence analysis estimating condition number system. Several experiments validate estimates, showing scalability quasi-optimality proposed. Moreover, solver exhibits robust behavior with respect shape polygonal elements. also show that faster could achieved an easy implement coarse space, slightly larger than minimal one covered theory.