A Superconvergent Discontinuous Galerkin Method for Hyperbolic Problems on Tetrahedral Meshes

In this manuscript we present a superconvergent discontinuous Galerkin method equipped with an element residual error estimator applied to scalar first-order hyperbolic problems using tetrahedral meshes. We present a local error analysis to derive a discontinuous Galerkin orthogonality condition for...

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Bibliographic Details
Published in:Journal of scientific computing 2014, Vol.58 (1), p.203-248
Main Authors: Adjerid, Slimane, Mechai, Idir
Format: Article
Language:English
Subjects:
Algorithms
Basis functions
Computation
Computational Mathematics and Numerical Analysis
Discretization
Error analysis
Errors
Estimators
Galerkin method
Galerkin methods
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Ordinary differential equations
Orthogonality
Partial differential equations
Polynomials
Scalars
Tetrahedra
Tetrahedrons
Theoretical
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Summary:In this manuscript we present a superconvergent discontinuous Galerkin method equipped with an element residual error estimator applied to scalar first-order hyperbolic problems using tetrahedral meshes. We present a local error analysis to derive a discontinuous Galerkin orthogonality condition for the leading term of the discretization error and establish new superconvergence points, lines and surfaces. We also derive new basis functions spanning the error and propose an implicit error estimation procedure by solving a local problem on each tetrahedron. The DG method combined with the a posteriori error estimation procedure yields both accurate error estimates and O ( h p + 2 ) superconvergent solutions. Computations validate our theory.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-013-9735-7