A simple finite element method for linear hyperbolic problems

doi:10.1016/j.cam.2017.08.025

Title: A simple finite element method for linear hyperbolic problems

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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:

^[1]; Ye, Xiu ^[2]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
Univ. of Arkansas, Little Rock, AR (United States). Dept. of Mathematics

Publication Date:: 2017-09-14

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE; National Science Foundation (NSF)

OSTI Identifier:: 1407723

Alternate Identifier(s):: OSTI ID: 1495741

Grant/Contract Number:: AC05-00OR22725; DMS-1620016; ERKJE45

Resource Type:: 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.

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                    Mu, Lin, & Ye, Xiu. A simple finite element method for linear hyperbolic problems.  United States.  doi:https://doi.org/10.1016/j.cam.2017.08.025

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                    Mu, Lin, and Ye, Xiu. Thu .  
        "A simple finite element method for linear hyperbolic problems".  United States.  doi:https://doi.org/10.1016/j.cam.2017.08.025.  https://www.osti.gov/servlets/purl/1407723.

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@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         = {2017},

  month        = {9}

}

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DOI: https://doi.org/10.1016/j.cam.2017.08.025

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