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Higher-order Immersed Discontinuous Galerkin Slimane Adjerid and Tao Lin

Summary: Higher-order Immersed Discontinuous Galerkin
Slimane Adjerid and Tao Lin
Department of Mathematics
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061-0123
We propose new discontinuous finite element methods that can be
applied to one-dimensional elliptic problems with discontinuous coeffi-
cients. These methods are based on a class of higher degree immersed
finite element spaces and can be used with a mesh independent of the
location of coefficient discontinuity. Numerical experiments are pre-
sented to show that these methods can achieve optimal convergence
rates under both h and p refinements.
1 Introduction
It has been pointed out in the literature (for example, see [2]), that finite
element methods should be designed/empolyed according to the problem to
be solved. For boundary value problems (BVPs) with discontinuous coef-
ficients, the conventional (including discontinuous Galerkin) finite element
methods employ universal basis functions, but they have to be used with a


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


Collections: Mathematics