Spectral Based Discontinuous Galerkin Reduced Basis Element Method for Parametrized Stokes Problems

07/2016

Spectral Based Discontinuous Galerkin Reduced Basis Element Method for Parametrized Stokes Problems

Friday 19th February 2016

Pacciarini, P.; Gervasio, P.; Quarteroni, A.

In this work we extend to the Stokes problem the Discontinuous Galerkin Reduced Basis Element (DGRBE) method introduced in [1]. By this method we aim at reducing the computational cost for the approximation of a parametrized Stokes problem on a domain partitioned into subdomains. During an offline stage, expensive but performed only once, a low-dimensional approximation space is built on each subdomain. For any new value of the parameter, the rapid evaluation of the solution takes place during the online stage and consists in a Galerkin projection onto the low-dimensional subspaces computed offline. The high-fidelity discretization on each subdomain, used to build the local low-dimensional subspaces, is based on spectral element methods. The continuity of both the velocity and the normal component of the Cauchy stress tensor at subdomain interfaces is weakly enforced by a discontinuous Galerkin approach.