论文信息 - Energy norm a posteriori error estimation for discontinuous Galerkin methods

Energy norm a posteriori error estimation for discontinuous Galerkin methods

In this paper we present a residual-based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous Galerkin approximations of elliptic problems. The theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed. We also present some illustrating numerical examples.

[1] Carsten Carstensen,et al. A posteriori error estimates for nonconforming finite element methods , 2002, Numerische Mathematik.

[2] L. R. Scott,et al. The Mathematical Theory of Finite Element Methods , 1994 .

[3] Mats G. Larson,et al. Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case , 2004, Numerische Mathematik.

[4] John B. Shoven,et al. I , Edinburgh Medical and Surgical Journal.

[5] I. Babuska,et al. A DiscontinuoushpFinite Element Method for Diffusion Problems , 1998 .

[6] Mats G. Larson,et al. Analysis of a Nonsymmetric Discontinuous Galerkin Method for Elliptic Problems: Stability and Energy Error Estimates , 2004, SIAM J. Numer. Anal..

[7] Vivette Girault,et al. Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[8] P. Hansbo,et al. A finite element method for domain decomposition with non-matching grids , 2003 .

[9] J. Nitsche. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind , 1971 .

[10] R. Durán,et al. A posteriori error estimators for nonconforming finite element methods , 1996 .