Accession Number : ADA301760

Title :   The Partition of Unity Finite Element Method

Descriptive Note : Final rept. Apr-Jun 95,

Corporate Author : MARYLAND UNIV COLLEGE PARK INST FOR PHYSICAL SCIENCE AND TECHNOLOGY

Personal Author(s) : Babuska, I. ; Melenk, J. M.

PDF Url : ADA301760

Report Date : JUN 1995

Pagination or Media Count : 38

Abstract : A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved. This new method can therefore be more efficient than the usual finite element methods. An additional feature of the partition-of-unity finite element method is that finite element spaces of any desired regularity can be constructed very easily. Moreover the method is of "meshless" type. This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers. The basic estimates for a-posteriori error estimation for this new method are also proved. (AN)

Descriptors :   *FINITE ELEMENT ANALYSIS, *APPROXIMATION(MATHEMATICS), OPTIMIZATION, MATRICES(MATHEMATICS), BOUNDARY LAYER, ESTIMATES, ERRORS, POLYNOMIALS, INTERPOLATION, PARTIAL DIFFERENTIAL EQUATIONS, CONVERGENCE, NUMERICAL METHODS AND PROCEDURES, LAPLACE TRANSFORMATION, HARMONIC ANALYSIS, HELMHOLTZ EQUATIONS.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE