Generalized multiscale finite element method. Symmetric interior penalty coupling Academic Article uri icon

abstract

  • Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. 2013 Elsevier Inc.

published proceedings

  • JOURNAL OF COMPUTATIONAL PHYSICS

altmetric score

  • 0.25

author list (cited authors)

  • Efendiev, Y., Galvis, J., Lazarov, R., Moon, M., & Sarkis, M.

citation count

  • 42

complete list of authors

  • Efendiev, Y||Galvis, J||Lazarov, R||Moon, M||Sarkis, M

publication date

  • January 1, 2013 11:11 AM