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Title: A simple finite element method for linear hyperbolic problems

Abstract

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

Authors:
ORCiD logo [1];  [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
  2. Univ. of Arkansas, Little Rock, AR (United States). Dept. of Mathematics
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1407723
Grant/Contract Number:  
AC05-00OR22725; DMS-1620016
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 330; Journal Issue: C; Journal ID: ISSN 0377-0427
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Finite element methods; Hyperbolic equations

Citation Formats

Mu, Lin, and Ye, Xiu. A simple finite element method for linear hyperbolic problems. United States: N. p., 2017. Web. doi:10.1016/j.cam.2017.08.025.
Mu, Lin, & Ye, Xiu. A simple finite element method for linear hyperbolic problems. United States. doi:10.1016/j.cam.2017.08.025.
Mu, Lin, and Ye, Xiu. Thu . "A simple finite element method for linear hyperbolic problems". United States. doi:10.1016/j.cam.2017.08.025. https://www.osti.gov/servlets/purl/1407723.
@article{osti_1407723,
title = {A simple finite element method for linear hyperbolic problems},
author = {Mu, Lin and Ye, Xiu},
abstractNote = {Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.},
doi = {10.1016/j.cam.2017.08.025},
journal = {Journal of Computational and Applied Mathematics},
number = C,
volume = 330,
place = {United States},
year = {Thu Sep 14 00:00:00 EDT 2017},
month = {Thu Sep 14 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
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