TY - JOUR

T1 - Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations

AU - Dobrev, Veselin A.

AU - Lazarov, Raytcho D.

AU - Vassilevski, Panayot S.

AU - Zikatanov, Ludmil T.

PY - 2006/11

Y1 - 2006/11

N2 - This paper reviews some known and proposes some new preconditioning methods for a number of discontinuous Galerkin (or DG) finite element approximations for elliptic problems of second order. Nested hierarchy of meshes is generally assumed. Our approach utilizes a general two-level scheme, where the finite element space for the DG method is decomposed into a subspace (viewed as an auxiliary or 'coarse' space), plus a correction which can be handled by a standard smoothing procedure. We consider three different auxiliary subspaces, namely, piecewise linear C0-conforming functions, piecewise linear functions that are continuous at the centroids of the edges/faces (Crouzeix-Raviart finite elements) and piecewise constant functions over the finite elements. To support the theoretical results, we also present numerical experiments for 3-D model problem showing uniform convergence of the constructed methods.

AB - This paper reviews some known and proposes some new preconditioning methods for a number of discontinuous Galerkin (or DG) finite element approximations for elliptic problems of second order. Nested hierarchy of meshes is generally assumed. Our approach utilizes a general two-level scheme, where the finite element space for the DG method is decomposed into a subspace (viewed as an auxiliary or 'coarse' space), plus a correction which can be handled by a standard smoothing procedure. We consider three different auxiliary subspaces, namely, piecewise linear C0-conforming functions, piecewise linear functions that are continuous at the centroids of the edges/faces (Crouzeix-Raviart finite elements) and piecewise constant functions over the finite elements. To support the theoretical results, we also present numerical experiments for 3-D model problem showing uniform convergence of the constructed methods.

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U2 - 10.1002/nla.504

DO - 10.1002/nla.504

M3 - Article

AN - SCOPUS:33750694584

SN - 1070-5325

VL - 13

SP - 753

EP - 770

JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

IS - 9

ER -