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Summary: c 2011
011
Adaptive discontinuous Galerkin methods in
multiwavelets bases
Rick Archibald
George Fann
William Shelton
Abstract
We use a multiwavelet basis with the Discontinuous Galerkin (DG) method to pro-
duce a multi-scale DG method. We apply this Multiwavelet DG method to convection
and convection-diffusion problems in multiple dimensions. Merging the DG method
with multiwavelets allows the adaptivity in the DG method to be resolved through
manipulation of multiwavelet coefficients rather than grid manipulation. Additionally,
the Multiwavelet DG method is tested on non-linear equations in one dimension and
on the cubed sphere.
Key Words: Multiwavelets, Discontinuous Galerkin
1 Introduction
The discontinuous Galerkin (DG) method is a finite element method that is locally conserva-
tive and stable with high-order accuracy. The DG formulation utilizes an elementwise discon-
tinuous approximation, where numerical information only passes locally through numerical
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