Spectral based Discontinuous Galerkin Reduced Basis Element method for parametrized Stokes problems. (October 2016)

• Record Type: Journal Article
• Authors: Pacciarini, Paolo; Gervasio, Paola; Quarteroni, Alfio
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 8(2016)
• Page Start: 1977
• Page End: 1987
• Publication Date: 2016-10
• Subjects: Reduced Basis Element method -- Discontinuous Galerkin -- Domain decomposition -- Spectral element methods -- Parametrized PDE -- Stokes equations; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.01.030
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this work we extend to the Stokes problem the Discontinuous Galerkin Reduced Basis Element (DGRBE) method introduced in Antonietti et al. (2015). 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.