Finite Element Solution to the Helmholtz Equation with High Wave Number. Part 2. The h-p Version of the FEM

In this paper, which is part 2 in a series of two, the investigation of the Galerkin finite element solution to the Helmholtz equation is continued. While part 1 contained results on the h-version with piecewise linear approximation, the present part deals with approximation spaces of order p greate...

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Bibliographic Details
Main Authors: Ihlenburg, Frank, Babuska, Ivo M
Format: Report
Language:English
Subjects:
APPROXIMATION(MATHEMATICS)
ASYMPTOTIC NORMALITY
BOUNDARY VALUE PROBLEMS
DIFFERENTIAL EQUATIONS
DIRICHLET BOUNDARY CONDITIONS
ERROR ANALYSIS
ESTIMATES
FINITE DIFFERENCE THEORY
FINITE ELEMENT ANALYSIS
GALERKIN METHOD
GREENS FUNCTIONS
HELMHOLTZ EQUATION
MATHEMATICAL MODELS
Numerical Mathematics
NUMERICAL METHODS AND PROCEDURES
PROBLEM SOLVING
SOLUTIONS(GENERAL)
STABILITY
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Summary:In this paper, which is part 2 in a series of two, the investigation of the Galerkin finite element solution to the Helmholtz equation is continued. While part 1 contained results on the h-version with piecewise linear approximation, the present part deals with approximation spaces of order p greater than or equal 1. The method is assumed to be uniform both w.r. to h and p. The results are presented on a one-dimensional model problem with Dirichlet/Robin boundary conditions. In particular there are proven stability estimates, both w.r. to data of higher regularity and data that is bounded in lower norms. (AN)