Explicit finite element methods for symmetric hyperbolic equations

被引：78

作者：

Falk, RS ^{[1
]}

Richter, GR

机构：

[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[2] Rutgers State Univ, Dept Comp Sci, Piscataway, NJ 08854 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 1999年 / 36卷 / 03期

关键词：

finite elements; symmetric hyperbolic; explicit;

D O I：

10.1137/S0036142997329463

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A family of explicit space-time finite element methods for the initial boundary value problem for linear, symmetric hyperbolic systems of equations is described and analyzed. The method generalizes the discontinuous Galerkin method and, as is typical for this method, obtains error estimates of order O(h(n+1/2)) for approximations by polynomials of degree less than or equal to n.

引用

页码：935 / 952

页数：18

共 13 条

[1] A LOW DISPERSION, HIGH-ACCURACY FINITE-ELEMENT METHOD FOR 1ST ORDER HYPERBOLIC SYSTEMS IN SEVERAL SPACE VARIABLES [J].

DU, Q ;

GUNZBURGER, M ;

LAYTON, W .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1988, 15 (6-8) :447-457

[2] SYMMETRIC POSITIVE LINEAR DIFFERENTIAL EQUATIONS [J].

FRIEDRICHS, KO .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1958, 11 (03) :333-418

[3]

GUNZBURGER MD, 1977, MATH COMPUT, V31, P661, DOI 10.1090/S0025-5718-1977-0436624-0

[4]

JOHNSON C, 1986, MATH COMPUT, V46, P1, DOI 10.1090/S0025-5718-1986-0815828-4

[5] FINITE-ELEMENT METHODS FOR LINEAR HYPERBOLIC PROBLEMS [J].

JOHNSON, C ;

NAVERT, U ;

PITKARANTA, J .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1984, 45 (1-3) :285-312

[6] HIGH-ACCURACY FINITE-ELEMENT METHODS FOR POSITIVE SYMMETRICAL-SYSTEMS [J].

LAYTON, W .

COMPUTERS & MATHEMATICS WITH APPLICATIONS-PART A, 1986, 12 (4-5) :565-579

[7] STABLE GALERKIN METHODS FOR HYPERBOLIC SYSTEMS [J].

LAYTON, WJ .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (02) :221-233

[8] FINITE-ELEMENT METHODS FOR SYMMETRIC HYPERBOLIC EQUATIONS [J].

LESAINT, P .

NUMERISCHE MATHEMATIK, 1973, 21 (03) :244-255

[9]

Lesaint P., 1974, Mathematical Aspects of Finite Elements in Partial Differential Equations, DOI DOI 10.1016/B978-0-12-208350-1.50008-X

[10] A NOTE ON THE CONVERGENCE OF THE DISCONTINUOUS GALERKIN METHOD FOR A SCALAR HYPERBOLIC EQUATION [J].

PETERSON, TE .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1991, 28 (01) :133-140

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