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Title: One-sided Post-processing for the Discontinuous Galerkin Method Using ENO Type Stencil Choosing and the Local Edge Detection Method

Abstract

In a previous paper by Ryan and Shu [Ryan, J. K., and Shu, C.-W. (2003). Methods Appl. Anal. 10(2), 295-307], a one-sided post-processing technique for the discontinuous Galerkin method was introduced for reconstructing solutions near computational boundaries and discontinuities in the boundaries, as well as for changes in mesh size. This technique requires prior knowledge of the discontinuity location in order to determine whether to use centered, partially one-sided, or one-sided post-processing. We now present two alternative stencil choosing schemes to automate the choice of post-processing stencil. The first is an ENO type stencil choosing procedure, which is designed to choose centered post-processing in smooth regions and one-sided or partially one-sided post-processing near a discontinuity, and the second method is based on the edge detection method designed by Archibald, Gelb, and Yoon [Archibald, R., Gelb, A., and Yoon, J. (2005). SIAM J. Numeric. Anal. 43, 259-279; Archibald, R., Gelb, A., and Yoon, J. (2006). Appl. Numeric. Math. (submitted)]. We compare these stencil choosing techniques and analyze their respective strengths and weaknesses. Finally, the automated stencil choices are applied in conjunction with the appropriate post-processing procedures and it is determine that the resulting numerical solutions are of the correct order.

Authors:
 [1];  [2];  [3];  [4]
  1. ORNL
  2. Arizona State University
  3. University of Massachusetts Dartmouth
  4. Virginia Polytechnic Institute and State University (Virginia Tech)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Center for Computational Sciences
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
930797
DOE Contract Number:  
DE-AC05-00OR22725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Scientific Computing; Journal Volume: 28; Journal Issue: 2-3
Country of Publication:
United States
Language:
English
Subject:
97; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; GALERKIN-PETROV METHOD; DATA PROCESSING; NUMERICAL SOLUTION

Citation Formats

Archibald, Richard K, Gelb, Anne, Gottlieb, Sigal, and Ryan, Jennifer. One-sided Post-processing for the Discontinuous Galerkin Method Using ENO Type Stencil Choosing and the Local Edge Detection Method. United States: N. p., 2006. Web. doi:10.1007/s10915-006-9090-z.
Archibald, Richard K, Gelb, Anne, Gottlieb, Sigal, & Ryan, Jennifer. One-sided Post-processing for the Discontinuous Galerkin Method Using ENO Type Stencil Choosing and the Local Edge Detection Method. United States. doi:10.1007/s10915-006-9090-z.
Archibald, Richard K, Gelb, Anne, Gottlieb, Sigal, and Ryan, Jennifer. Sun . "One-sided Post-processing for the Discontinuous Galerkin Method Using ENO Type Stencil Choosing and the Local Edge Detection Method". United States. doi:10.1007/s10915-006-9090-z.
@article{osti_930797,
title = {One-sided Post-processing for the Discontinuous Galerkin Method Using ENO Type Stencil Choosing and the Local Edge Detection Method},
author = {Archibald, Richard K and Gelb, Anne and Gottlieb, Sigal and Ryan, Jennifer},
abstractNote = {In a previous paper by Ryan and Shu [Ryan, J. K., and Shu, C.-W. (2003). Methods Appl. Anal. 10(2), 295-307], a one-sided post-processing technique for the discontinuous Galerkin method was introduced for reconstructing solutions near computational boundaries and discontinuities in the boundaries, as well as for changes in mesh size. This technique requires prior knowledge of the discontinuity location in order to determine whether to use centered, partially one-sided, or one-sided post-processing. We now present two alternative stencil choosing schemes to automate the choice of post-processing stencil. The first is an ENO type stencil choosing procedure, which is designed to choose centered post-processing in smooth regions and one-sided or partially one-sided post-processing near a discontinuity, and the second method is based on the edge detection method designed by Archibald, Gelb, and Yoon [Archibald, R., Gelb, A., and Yoon, J. (2005). SIAM J. Numeric. Anal. 43, 259-279; Archibald, R., Gelb, A., and Yoon, J. (2006). Appl. Numeric. Math. (submitted)]. We compare these stencil choosing techniques and analyze their respective strengths and weaknesses. Finally, the automated stencil choices are applied in conjunction with the appropriate post-processing procedures and it is determine that the resulting numerical solutions are of the correct order.},
doi = {10.1007/s10915-006-9090-z},
journal = {Journal of Scientific Computing},
number = 2-3,
volume = 28,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 2006},
month = {Sun Jan 01 00:00:00 EST 2006}
}