Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

A Discontinuous Galerkin Finite Element Method for Time Dependent Partial Differential Equations with Higher Order Derivatives

Yingda Cheng and Chi-Wang Shu
Mathematics of Computation
Vol. 77, No. 262 (Apr., 2008), pp. 699-730
Stable URL: http://www.jstor.org/stable/40234530
Page Count: 32
  • Read Online (Free)
  • Download ($34.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Discontinuous Galerkin Finite Element Method for Time Dependent Partial Differential Equations with Higher Order Derivatives
Preview not available

Abstract

In this paper, we develop a new discontinuous Galerkin (DG) finite element method for solving time dependent partial differential equations (PDEs) with higher order spatial derivatives. Unlike the traditional local discontinuous Galerkin (LDG) method, the method in this paper can be applied without introducing any auxiliary variables or rewriting the original equation into a larger system. Stability is ensured by a careful choice of interface numerical fluxes. The method can be designed for quite general nonlinear PDEs and we prove stability and give error estimates for a few representative classes of PDEs up to fifth order. Numerical examples show that our scheme attains the optimal (k + l)-th order of accuracy when using piecewise k-th degree polynomials, under the condition that k + 1 is greater than or equal to the order of the equation.

Page Thumbnails

  • Thumbnail: Page 
699
    699
  • Thumbnail: Page 
700
    700
  • Thumbnail: Page 
701
    701
  • Thumbnail: Page 
702
    702
  • Thumbnail: Page 
703
    703
  • Thumbnail: Page 
704
    704
  • Thumbnail: Page 
705
    705
  • Thumbnail: Page 
706
    706
  • Thumbnail: Page 
707
    707
  • Thumbnail: Page 
708
    708
  • Thumbnail: Page 
709
    709
  • Thumbnail: Page 
710
    710
  • Thumbnail: Page 
711
    711
  • Thumbnail: Page 
712
    712
  • Thumbnail: Page 
713
    713
  • Thumbnail: Page 
714
    714
  • Thumbnail: Page 
715
    715
  • Thumbnail: Page 
716
    716
  • Thumbnail: Page 
717
    717
  • Thumbnail: Page 
718
    718
  • Thumbnail: Page 
719
    719
  • Thumbnail: Page 
720
    720
  • Thumbnail: Page 
721
    721
  • Thumbnail: Page 
722
    722
  • Thumbnail: Page 
723
    723
  • Thumbnail: Page 
724
    724
  • Thumbnail: Page 
725
    725
  • Thumbnail: Page 
726
    726
  • Thumbnail: Page 
727
    727
  • Thumbnail: Page 
728
    728
  • Thumbnail: Page 
729
    729
  • Thumbnail: Page 
730
    730