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A Discontinuous Galerkin Method for Higher-order
 

Summary: A Discontinuous Galerkin Method for
Higher-order
Differential Equations
Slimane Adjerid and Helmi Temimi
Department of Mathematics
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061-0123
March 19, 2006
Abstract
In this paper we propose a new discontinuous finite element method
for higher-order initial value problems where the finite element solu-
tion exhibits an optimal O(tp+1) convergence rate in the L2 norm.
We further show that the p-degree discontinuous solution of differen-
tial equation of order m and its first m-1 derivatives are O(t2p+2-m)
superconvergent at the end of each step. We also establish that the
p-degree discontinuous solution is O(tp+2) superconvergent at the
roots of (p + 1 - m)-degree Jacobi polynomial on each step. Finally,
we use these results to construct asymptotically correct a posteriori
error estimates and present several computational results to validate
the theory.

  

Source: Adjerid, Slimane - Department of Mathematics, Virginia Tech

 

Collections: Mathematics