 |
|
CCT-TR-2009-2
Title:
A New Error Analysis for Discontinuous Finite Element Methods for Linear Elliptic Problems
Authors:
Thirupathi Gudi, Center for Computation & Technology, Louisiana State University
Summary:
The standard a priori error analysis of discontinuous Galerkin methods requires additional regularity on the solution of the elliptic boundary value problem in order to justify the Galerkin orthogonality and to handle the normal derivative on element interfaces that appear in the discrete energy norm. In this paper, a new error analysis of discontinuous Galerkin methods is developed using only the Hk weak formulation of a boundary value problem of order 2k. This is accomplished by replacing the Galerkin orthogonality with estimates borrowed from a posteriori error analysis and by using a discrete energy norm that is well defined for functions in Hk.The standard a priori error analysis of discontinuous Galerkin methods requires additional regularity on the solution of the elliptic boundary value problem in order to justify the Galerkin orthogonality and to handle the normal derivative on element interfaces that appear in the discrete energy norm. In this paper, a new error analysis of discontinuous Galerkin methods is developed using only the Hk weak formulation of a boundary value problem of order 2k. This is accomplished by replacing the Galerkin orthogonality with estimates borrowed from a posteriori error analysis and by using a discrete energy norm that is well defined for functions in Hk.
Download Article:
CCT-TR-2009-2.pdf
|
|
|
|
 |
Print
this Page
Refer
this page to a friend
