Adaptive discontinuous Galerkin methods in multiwavelets bases

Rick Archibald; George Fann; William Shelton

doi:10.1016/j.apnum.2011.02.005

Adaptive discontinuous Galerkin methods in multiwavelets bases

Rick Archibald, George Fann, William Shelton

Data Analysis and Machine Learning

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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.

Original language	English
Pages (from-to)	879-890
Number of pages	12
Journal	Applied Numerical Mathematics
Volume	61
Issue number	7
DOIs	https://doi.org/10.1016/j.apnum.2011.02.005
State	Published - Jul 2011

Funding

The submitted manuscript has been authored by a contractor [UT-Battelle, manager of Oak Ridge National Laboratory (ORNL)] of the U.S. Government under Contract No. DE-AC05-00OR22725. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.

Funders	Funder number
U.S. Government	DE-AC05-00OR22725
Oak Ridge National Laboratory

Keywords

Discontinuous Galerkin
Multiwavelets

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10.1016/j.apnum.2011.02.005

Cite this

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AB - 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.

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Adaptive discontinuous Galerkin methods in multiwavelets bases

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Keywords

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