A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

• DOI: 10.1016/j.cma.2014.09.036
• Publication Date: 2014-10-22T16:51:48Z
• Authors: Yalchin Efendiev; Raytcho Lazarov; Minam Moon; Ke Shi
• Keywords: Multiscale finite element method; Mechanics of Materials; Mechanical Engineering; Spectral basis function; Computational Mechanics; Physics and Astronomy(all); 0101 mathematics; 01 natural sciences; Hybridizable discontinuous Galerkin; Computer Science Applications

Abstract We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.