Adaptive discontinuous Galerkin methods in multiwavelets bases

Authors:
Rick Archibald;George Fann;William Shelton
Affiliations:
Computer Science and Mathematics, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States;Computer Science and Mathematics, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States;Computer Science and Mathematics, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

We use a multiwavelet basis with the Discontinuous Galerkin (DG) method to produce 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.