The discontinuous Galerkin method for two-dimensional hyperbolic problems part II: A posteriori error estimation

Slimane Adjerid; Mahboub Baccouch

doi:10.1007/s10915-008-9222-8

The discontinuous Galerkin method for two-dimensional hyperbolic problems part II: A posteriori error estimation

Slimane Adjerid, Mahboub Baccouch

Mathematics

Research output: Contribution to journal › Article

35 Scopus citations

Abstract

In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar first-order hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each triangle is estimated by solving a local problem. We also show global superconvergence for discontinuous solutions on triangular meshes. The a posteriori error estimates are tested on several linear and nonlinear problems to show their efficiency and accuracy under mesh refinement for smooth and discontinuous solutions.

Original language	English (US)
Pages (from-to)	15-49
Number of pages	35
Journal	Journal of Scientific Computing
Volume	38
Issue number	1
DOIs	https://doi.org/10.1007/s10915-008-9222-8
State	Published - Jan 2009

Keywords

A posteriori error estimation
Discontinuous Galerkin method
Hyperbolic problems
Superconvergence

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
Engineering(all)
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s10915-008-9222-8

Fingerprint Dive into the research topics of 'The discontinuous Galerkin method for two-dimensional hyperbolic problems part II: A posteriori error estimation'. Together they form a unique fingerprint.

Cite this

Adjerid, S., & Baccouch, M. (2009). The discontinuous Galerkin method for two-dimensional hyperbolic problems part II: A posteriori error estimation. Journal of Scientific Computing, 38(1), 15-49. https://doi.org/10.1007/s10915-008-9222-8

@article{cac4ed73a237479785c7f7ed2946b2c9,

title = "The discontinuous Galerkin method for two-dimensional hyperbolic problems part II: A posteriori error estimation",

abstract = "In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar first-order hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each triangle is estimated by solving a local problem. We also show global superconvergence for discontinuous solutions on triangular meshes. The a posteriori error estimates are tested on several linear and nonlinear problems to show their efficiency and accuracy under mesh refinement for smooth and discontinuous solutions.",

keywords = "A posteriori error estimation, Discontinuous Galerkin method, Hyperbolic problems, Superconvergence",

author = "Slimane Adjerid and Mahboub Baccouch",

year = "2009",

month = jan,

doi = "10.1007/s10915-008-9222-8",

language = "English (US)",

volume = "38",

pages = "15--49",

journal = "Journal of Scientific Computing",

issn = "0885-7474",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - The discontinuous Galerkin method for two-dimensional hyperbolic problems part II

T2 - A posteriori error estimation

AU - Adjerid, Slimane

AU - Baccouch, Mahboub

PY - 2009/1

Y1 - 2009/1

N2 - In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar first-order hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each triangle is estimated by solving a local problem. We also show global superconvergence for discontinuous solutions on triangular meshes. The a posteriori error estimates are tested on several linear and nonlinear problems to show their efficiency and accuracy under mesh refinement for smooth and discontinuous solutions.

AB - In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar first-order hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each triangle is estimated by solving a local problem. We also show global superconvergence for discontinuous solutions on triangular meshes. The a posteriori error estimates are tested on several linear and nonlinear problems to show their efficiency and accuracy under mesh refinement for smooth and discontinuous solutions.

KW - A posteriori error estimation

KW - Discontinuous Galerkin method

KW - Hyperbolic problems

KW - Superconvergence

UR - http://www.scopus.com/inward/record.url?scp=59349090599&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=59349090599&partnerID=8YFLogxK

U2 - 10.1007/s10915-008-9222-8

DO - 10.1007/s10915-008-9222-8

M3 - Article

AN - SCOPUS:59349090599

VL - 38

SP - 15

EP - 49

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

IS - 1

ER -