TY - JOUR

T1 - Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem

AU - Adjerid, Slimane

AU - Baccouch, Mahboub

N1 - Funding Information:
This research was partially supported by the National Science Foundation (Grant Numbers DMS 0511806, DMS 0809262).

PY - 2010/9

Y1 - 2010/9

N2 - In this manuscript we investigate the global convergence of the implicit residual-based a posteriori error estimates of Adjerid et al. (2002) [3]. The authors used the discontinuous Galerkin method to solve one-dimensional transient hyperbolic problems and showed that the local error on each element is proportional to a Radau polynomial. The discontinuous Galerkin error estimates under investigation are computed by solving a local steady problem on each element. Here we prove that, for smooth solutions, these a posteriori error estimates at a fixed time t converge to the true spatial error in the L2 norm under mesh refinement.

AB - In this manuscript we investigate the global convergence of the implicit residual-based a posteriori error estimates of Adjerid et al. (2002) [3]. The authors used the discontinuous Galerkin method to solve one-dimensional transient hyperbolic problems and showed that the local error on each element is proportional to a Radau polynomial. The discontinuous Galerkin error estimates under investigation are computed by solving a local steady problem on each element. Here we prove that, for smooth solutions, these a posteriori error estimates at a fixed time t converge to the true spatial error in the L2 norm under mesh refinement.

KW - A posteriori error estimation

KW - Discontinuous Galerkin

KW - Hyperbolic problems

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U2 - 10.1016/j.apnum.2010.04.014

DO - 10.1016/j.apnum.2010.04.014

M3 - Article

AN - SCOPUS:77955662309

SN - 0168-9274

VL - 60

SP - 903

EP - 914

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 9

ER -