Efficient Preconditioning for Discontinuous Galerkin Method with Reconstructed Discontinuous Approximation

Abstract:

In this talk, I will introduce the reconstructed discontinuous approximation (RDA) method for solving second-order elliptic problem with an efficient preconditioner. The RDA method uses a reconstructed high-order approximation space which is constructed by solving a local constrained least squares problem. One attractive feature for the reconstructed space is that it has onlyone degree of freedom per element. This space can be directly used with the symmetric/nonsymmetric interior penalty discontinuous Galerkin method. Further, an efficient preconditioner can be constructed from the piecewise constant space. The upper bound of the condition number to the preconditioned symmetric/nonsymmetric system is shown to be independent of the mesh size. Numerical experiments areprovided to demonstrate the validity of the theory and the efficiency of the proposed method.