Hoellig, K.
Overview
Works:  5 works in 6 publications in 1 language and 7 library holdings 

Publication Timeline
.
Most widely held works by
K Hoellig
BSplines From Parallelepipeds by
Carl De Boor(
Book
)
2 editions published in 1982 in English and held by 3 WorldCat member libraries worldwide
Local support bases for piecewise polynomial spaces are important for applications such as finite element methods, data fitting etc. In (BH sub 1) a general construction principle for such Bsplines was described. A special case are the so called boxsplines. They have a particularly regular discontinuity pattern and coincide in special cases with standard finite elements. It is hoped that using translates of boxsplines will lead, at least in two variables, to a unified theory for piecewise polynomial functions on regular meshes. This note is a first attempt in this direction and deals with basic approximation properties of translates of one boxsplines such as stability, degree of approximation etc. (Author)
2 editions published in 1982 in English and held by 3 WorldCat member libraries worldwide
Local support bases for piecewise polynomial spaces are important for applications such as finite element methods, data fitting etc. In (BH sub 1) a general construction principle for such Bsplines was described. A special case are the so called boxsplines. They have a particularly regular discontinuity pattern and coincide in special cases with standard finite elements. It is hoped that using translates of boxsplines will lead, at least in two variables, to a unified theory for piecewise polynomial functions on regular meshes. This note is a first attempt in this direction and deals with basic approximation properties of translates of one boxsplines such as stability, degree of approximation etc. (Author)
Existence of Infinitely Many Solutions for a Forward Backward Heat Equation(
Book
)
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
This reprint presents a piecewise linear function which satisfies a certain condition and which is monotone decreasing on an interval. It is shown that in a certain case, there exists a certain condition that a initial boundary value problem has infinitely many solutions. Additional keywords: Parabolic equations; Nonlinear systems; Diffusion; Computations; and Army research
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
This reprint presents a piecewise linear function which satisfies a certain condition and which is monotone decreasing on an interval. It is shown that in a certain case, there exists a certain condition that a initial boundary value problem has infinitely many solutions. Additional keywords: Parabolic equations; Nonlinear systems; Diffusion; Computations; and Army research
Convergence of cardinal series by
Carl De Boor(
Book
)
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
The result of this paper is a generalization of an characterization of the limits of multivariate cardinal splines. Keywords: Convergence; fourier transforms; Analytic functions; Convolution; Exponential functions; Fourier series
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
The result of this paper is a generalization of an characterization of the limits of multivariate cardinal splines. Keywords: Convergence; fourier transforms; Analytic functions; Convolution; Exponential functions; Fourier series
C InfinityRegularity for the Porous Median Equation(
Book
)
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
The equation stated in the abstract describes the expansion of a gas in a one dimensional porous medium. While existence of weak solutions can be obtained by standard energy methods, not much was known about regularity of the solution near the free boundaries. The difficulty is that the equation degenerates at the boundary and the hyperbolic term becomes dominant. The authors show in this report that despite of the degeneracy the free boundary is smooth with the possible exception of a discontinuity in the derivative at the waiting time. Their method is based on energy estimates in weighted norms using some of the ideas in another document. Additional keywords: estimates, approximation(mathematics); finite difference theory; finite element analysis
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
The equation stated in the abstract describes the expansion of a gas in a one dimensional porous medium. While existence of weak solutions can be obtained by standard energy methods, not much was known about regularity of the solution near the free boundaries. The difficulty is that the equation degenerates at the boundary and the hyperbolic term becomes dominant. The authors show in this report that despite of the degeneracy the free boundary is smooth with the possible exception of a discontinuity in the derivative at the waiting time. Their method is based on energy estimates in weighted norms using some of the ideas in another document. Additional keywords: estimates, approximation(mathematics); finite difference theory; finite element analysis
Fundamental solutions for multivariate difference equations and applications to cardinal interpolation by
University of WisconsinMadison(
Book
)
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
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