Suli, Endre and Houston, P. and Schwab, Christoph (1999) hpFinite Element Methods for Hyperbolic Problems. Technical Report. Unspecified. (Submitted)

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Abstract
Presented as Invited Lecture at the 10th Conference on the Mathematics of Finite Elements and Applications, Brunel University, June 1999.
This paper is devoted to the a priori and a posteriori error analysis of the hpversion of the discontinuous Galerkin finite element method for partial differential equations of hyperbolic and nearlyhyperbolic character. We consider secondorder partial differential equations with nonnegative characteristic form, a large class of equations which includes convectiondominated diffusion problems, degenerate elliptic equations and secondorder problems of mixed elliptichyperbolicparabolic type. An a priori error bound is derived for the method in the socalled DGnorm which is optimal in terms of the mesh size h; the error bound is either 1 degree or 1/2 degree below optimal in terms of the polynomial degree p, depending on whether the problem is convectiondominated, or diffusiondominated, respectively. In the case of a firstorder hyperbolic equation the error bound is hpoptimal in the DGnorm. For firstorder hyperbolic problems, we also discuss the a posteriori error analysis of the method and implement the resulting bounds into an hpadaptive algorithm. The theoretical findings are illustrated by numerical experiments.
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1289 
Deposited By:  Lotti Ekert 
Deposited On:  02 Jun 2011 07:58 
Last Modified:  29 May 2015 18:59 
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