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

abstract

• 2014 Elsevier B.V. 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.

authors

• Efendiev, Yalchin
• Lazarov, Raytcho

published proceedings

• COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

author list (cited authors)

• Efendiev, Y., Lazarov, R., Moon, M., & Shi, K. e.

citation count

• 25

complete list of authors

• Efendiev, Yalchin||Lazarov, Raytcho||Moon, Minam||Shi, Ke

publication date

• January 2015

publisher

• Elsevier  Publisher

published in

• Computer Methods in Applied Mechanics and Engineering  Journal

keywords

• Hybridizable Discontinuous Galerkin
• Multiscale Finite Element Method
• Spectral Basis Function

Digital Object Identifier (DOI)

• 10.1016/j.cma.2014.09.036

start page

• 243

end page

• 256

volume

• 292

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.cma.2014.09.036