### Abstract

A finite element method for hyperbolic equations is analyzed in the context of a first order linear problem in R**2. The method is applicable over a triangulation of the domain, and produces a continuous piecewise polynomial approximation, which can be developed in an explicit fashion from triangle to triangle. In a sense, it extends the basic upwind difference scheme to higher order. The method is shown to be stable, and error estimates are obtained. For nth degree approximation, the errors in the approximate solution and its gradient are shown to be at least of order h**n** plus ** one quarter and h**n** minus ** one-half , respectively, assuming sufficient regularity in the solution.

Original language | English (US) |
---|---|

Pages (from-to) | 257-278 |

Number of pages | 22 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1987 |

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### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Journal on Numerical Analysis*,

*24*(2), 257-278. https://doi.org/10.1137/0724021

}

*SIAM Journal on Numerical Analysis*, vol. 24, no. 2, pp. 257-278. https://doi.org/10.1137/0724021

**ANALYSIS OF A CONTINUOUS FINITE ELEMENT METHOD FOR HYPERBOLIC EQUATIONS.** / Falk, Richard S.; Richter, Gerard R.

Research output: Contribution to journal › Article

TY - JOUR

T1 - ANALYSIS OF A CONTINUOUS FINITE ELEMENT METHOD FOR HYPERBOLIC EQUATIONS.

AU - Falk, Richard S.

AU - Richter, Gerard R.

PY - 1987/1/1

Y1 - 1987/1/1

N2 - A finite element method for hyperbolic equations is analyzed in the context of a first order linear problem in R**2. The method is applicable over a triangulation of the domain, and produces a continuous piecewise polynomial approximation, which can be developed in an explicit fashion from triangle to triangle. In a sense, it extends the basic upwind difference scheme to higher order. The method is shown to be stable, and error estimates are obtained. For nth degree approximation, the errors in the approximate solution and its gradient are shown to be at least of order h**n** plus ** one quarter and h**n** minus ** one-half , respectively, assuming sufficient regularity in the solution.

AB - A finite element method for hyperbolic equations is analyzed in the context of a first order linear problem in R**2. The method is applicable over a triangulation of the domain, and produces a continuous piecewise polynomial approximation, which can be developed in an explicit fashion from triangle to triangle. In a sense, it extends the basic upwind difference scheme to higher order. The method is shown to be stable, and error estimates are obtained. For nth degree approximation, the errors in the approximate solution and its gradient are shown to be at least of order h**n** plus ** one quarter and h**n** minus ** one-half , respectively, assuming sufficient regularity in the solution.

UR - http://www.scopus.com/inward/record.url?scp=0023329117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023329117&partnerID=8YFLogxK

U2 - 10.1137/0724021

DO - 10.1137/0724021

M3 - Article

AN - SCOPUS:0023329117

VL - 24

SP - 257

EP - 278

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 2

ER -