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

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

Received date: 2020-10-26

  Revised date: 2021-01-08

  Online published: 2022-04-29

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.

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.

Cite this article

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 . DOI: 10.1007/s42967-021-00121-w

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