Title

Applicability of the Finite Element Concept to Hyperbolic Equations

Date

1980

Index Abstract

Coming Soon

Photo Quality

Not Needed

Report Number

AFWAL TR 80-3048

Creator

Guderly, K. G.

Clemm, Donald S

Corporate Author

University of Dayton Research institute; Flight Dynamics Laboratory

Date Issued

1980-06-01

Extent

140

Identifier

ADA089774

Distribution Classification

1

Contract

AFOSR 78-3524

DoD Project

2304

DoD Task

2304N1

DTIC Record Exists

No

Distribution Change Authority Correspondence

None

Abstract

The report analyses by means of examples the applicability of the finite element method (in the form of a weighted residual approach) to hyperbolic equations, using rectangular elements and bi-linear, bi-quadratic or bi-cubic shape functions. For sinusoidal initial conditions the errors are discussed for semi and fully discretized approximating equations. All methods have appreciable errors if the wave lengths are short. For semi-discretized methods, higher order elements give more accurate results at intermediate wave lengths. The fully discretized version for cubic elements becomes unstable, unless it is carried out as a combination of collocation and weighted residual methods. An example of a different kind shows the character of perturbations as one approaches the sonic line. A rationale for the choice of weight functions can be obtained by relating them to the Green's function. In two-dimensional problems, one can improve the cancellation of long distance effects of truncation errors by choosing characteristics as element boundaries.

Report Availability

Full text available by request

Provenance

IIT

Type

report