Capitalizing on Superconvergence for More Accurate Multi-Resolution Discontinuous Galerkin Methods

doi:10.1007/s42967-021-00121-w

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (2): 417-436.doi: 10.1007/s42967-021-00121-w

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Capitalizing on Superconvergence for More Accurate Multi-Resolution Discontinuous Galerkin Methods

Jennifer K. Ryan

Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80401, USA

收稿日期:2020-10-26 修回日期:2021-01-08 出版日期:2022-06-20 发布日期:2022-04-29
通讯作者: Jennifer K. Ryan E-mail:jkryan@mines.edu
基金资助:
This work was motivated by discussions with Dr. Venke Sankaran (Edwards Air Force Research Lab, USA) and was performed while visiting the Applied Mathematics group at HeinrichHeine University, Düsseldorf, Germany. Research supported by the Air Force Ofce of Scientifc Research (AFOSR) Computational Mathematics Program (Program Manager:Dr. Fariba Fahroo) under Grant numbers FA9550-18-1-0486 and FA9550-19-S-0003.

Capitalizing on Superconvergence for More Accurate Multi-Resolution Discontinuous Galerkin Methods

Jennifer K. Ryan

Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80401, USA

Received:2020-10-26 Revised:2021-01-08 Online:2022-06-20 Published:2022-04-29
Contact: Jennifer K. Ryan E-mail:jkryan@mines.edu
Supported by:
This work was motivated by discussions with Dr. Venke Sankaran (Edwards Air Force Research Lab, USA) and was performed while visiting the Applied Mathematics group at HeinrichHeine University, Düsseldorf, Germany. Research supported by the Air Force Ofce of Scientifc Research (AFOSR) Computational Mathematics Program (Program Manager:Dr. Fariba Fahroo) under Grant numbers FA9550-18-1-0486 and FA9550-19-S-0003.

摘要/Abstract

摘要： This article focuses on exploiting superconvergence to obtain more accurate multi-resolution analysis. Specifcally, we concentrate on enhancing the quality of passing of information between scales by implementing the Smoothness-Increasing Accuracy-Conserving (SIAC) fltering combined with multi-wavelets. This allows for a more accurate approximation when passing information between meshes of diferent resolutions. Although this article presents the details of the SIAC flter using the standard discontinuous Galerkin method, these techniques are easily extendable to other types of data.

关键词: Multi-resolution analysis, Multi-wavelets, Discontinuous Galerkin, Smoothness-Increasing Accuracy-Conserving (SIAC), Post-processing, Superconvergence, Accuracy enhancement

Abstract: This article focuses on exploiting superconvergence to obtain more accurate multi-resolution analysis. Specifcally, we concentrate on enhancing the quality of passing of information between scales by implementing the Smoothness-Increasing Accuracy-Conserving (SIAC) fltering combined with multi-wavelets. This allows for a more accurate approximation when passing information between meshes of diferent resolutions. Although this article presents the details of the SIAC flter using the standard discontinuous Galerkin method, these techniques are easily extendable to other types of data.

Key words: Multi-resolution analysis, Multi-wavelets, Discontinuous Galerkin, Smoothness-Increasing Accuracy-Conserving (SIAC), Post-processing, Superconvergence, Accuracy enhancement

中图分类号:

65M60

Jennifer K. Ryan. Capitalizing on Superconvergence for More Accurate Multi-Resolution Discontinuous Galerkin Methods[J]. Communications on Applied Mathematics and Computation, 2022, 4(2): 417-436.

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Capitalizing on Superconvergence for More Accurate Multi-Resolution Discontinuous Galerkin Methods

Capitalizing on Superconvergence for More Accurate Multi-Resolution Discontinuous Galerkin Methods

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