Computational aspects of the local discontinuous Galerkin method on unstructured grids in three dimensions

Using tensor notation, a simplified description of the most relevant operators of the local discontinuous Galerkin (LDG) method applied to a general elliptic boundary value problem on unstructured meshes in three dimensions is presented. A reduction of storage is achieved by introducing a fast algor...

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Bibliographic Details
Published inMathematical and computer modelling Vol. 57; no. 9-10; pp. 2279 - 2288
Main Authors Castillo, P.E., Sequeira, F.A.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.05.2013
Subjects
Discontinuous finite element methods
High-order approximations
Multilevel techniques
High-order approximations
Multilevel techniques
Discontinuous finite element methods
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Summary:Using tensor notation, a simplified description of the most relevant operators of the local discontinuous Galerkin (LDG) method applied to a general elliptic boundary value problem on unstructured meshes in three dimensions is presented. A reduction of storage is achieved by introducing a fast algorithm for the assembly of the Schur complement. A semi-algebraic multilevel preconditioner for low-order approximations using the classical Lagrange interpolatory basis is discussed. A series of numerical experiments is presented to illustrate the performance of the proposed preconditioning technique and accuracy of the method on three-dimensional problems.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.07.032