W. Wendland | Universität Stuttgart (original) (raw)
Papers by W. Wendland
Deutsche Gesellschaft für Luft- und Raumfahrt - Lilienthal-Oberth e.V., Bonn, 1988
Mathematical Methods in the Applied Sciences, 1986
In this paper, asymptotic expansions with respect to small Reynolds numbers are proved for the sl... more In this paper, asymptotic expansions with respect to small Reynolds numbers are proved for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid past a single plane wall. The flow problem is modelled by a certain boundary value problem for the stationary, nonlinear Navier-Stokes equations. The coefficients of these expansions are the solutions of various, linear Stokes problems which can be constructed by single layer potentials and corresponding boundary integral equations on the boundary surface of the particle. Furthermore, some asymptotic estimates at small Reynolds numbers are presented for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid between two parallel, plane walls and in an infinitely long, rectilinear cylinder of arbitrary cross section. In the case of the flow problem with a single plane wall, the paper is based on a thesis, which the author has written under the guidance of Professor Dr. Wolfgang L. Wendland.
Mathematical Methods in the Applied Sciences, 1989
Error estimates are shown for some spatially discrete Galerkin finite element methods for a non‐l... more Error estimates are shown for some spatially discrete Galerkin finite element methods for a non‐linear heat equation. The approximation schemes studied are based on the introduction of the enthalpy as a new dependent variable, and also on the application of the Kirchhoff transformation and on interpolation of the non‐linear coefficients into standard Lagrangian finite element spaces.
Lecture Notes in Mathematics, 1972
Zeitschrift für die gesamte innere Medizin und ihre Grenzgebiete, 1963
Archiv für experimentelle Veterinärmedizin, 1967
Mathematical Methods in the Applied Sciences, 1982
Data processing is an important tool in airspace surveillance and air traffic control today. In t... more Data processing is an important tool in airspace surveillance and air traffic control today. In this paper the problem is treated how to reconstruct a flown trajectory from its correlated radar plots subject to a certain knowledge of the aircraft manoeuverability and the radar measurement statistics. A variational approach leads to a generalized smoothing spline method. Simulation results are presented. 2 Mathematische Problemstellung Mit Hilfe eines konventionellen Drehradars werden normalenveise zweidimensionale Radardaten zu diskreten Zeitpunkten empfangen, die dann durch
Applicable Analysis, 1979
In this paper we develop a method for the approximation of a broad class of operator equations by... more In this paper we develop a method for the approximation of a broad class of operator equations by reproducing kernels. The relevant operators are defined on Hilbert spaces. Necessary and sufficient conditions for the convergence of the approximation are discussed in detail. The results can be applied-for example-to Fredholm integral operators of the first and second kind and to ordinary and partial differential operators of elliptic type. In this context we refer to [9] for methods to construct reproducing kernels.
Mathematical Methods in the Applied Sciences, 2000
2 collects the dimensionless conservative variables, with the density, v"(v , v)2 the velocity ve... more 2 collects the dimensionless conservative variables, with the density, v"(v , v)2 the velocity vector and e the total energy. The inviscid (Euler) #uxes f G and the viscous terms R G describe the convective and the viscous parts, Coupled Boundary Value Problems 403
Engineering Analysis with Boundary Elements, 1987
Engineering Analysis with Boundary Elements, 1987
Discrete and Continuous Dynamical Systems, 2004
Computing, 1992
The Approximation of Closed Manifolds by Triangulated Manifolds and the Triangulation of Closed M... more The Approximation of Closed Manifolds by Triangulated Manifolds and the Triangulation of Closed Manifolds. Let Fbe a closed surface in ~3. We assume Fis given by the local parameter representation f~:g2~ 3 , i= 1...p, (1.1) as a two-dimensional topological manifold, where f2~ c L~ 2 are open domains of the parameter plane.
Calcolo, 2003
Multidimensional surface potentials associated with elliptic differential operators are defined b... more Multidimensional surface potentials associated with elliptic differential operators are defined by surface integrals involving fundamental solutions of the differential operators which become singular when the observation point approaches the surface. Here we combine the choice of basis functions for the so-called approximate approximation of the surface layer density with the integration of the basis functions over the tangential space by the use of appropriate asymptotic expansions. Our approach leads to cubature formulae involving only nodes of a regular grid. These formulae turn out to be extremely efficient provided the saturation error of the approximate approximation is a priori chosen sufficiently small.
Applicable Analysis, 1979
In this paper we are concerned with the stability of the algebraic multiplicity of eigenvalues of... more In this paper we are concerned with the stability of the algebraic multiplicity of eigenvalues of holomorphic operator-valued functions in the framework of a generalized perturbation theory which is at the same time well-suited for the treatment of approximation methods. It is shown that the algebraic multiplicity of an isolated eigenvalue is stable if the operators under consideration are restricted to the class of so-called approximation-proper families of holomorphic functions of Fredholm mappings acting in certain discrete approximations. As an essential tool in this context the representation formula for the algebraic multiplicity of A. S. Markus and E. I. Sigal is used. The above problem has been rigorously studied in the case when the eigenvalue parameter occurs linearly, but even in this case our result is of interest.
Applicable Analysis, 1985
ABSTRACT
Deutsche Gesellschaft für Luft- und Raumfahrt - Lilienthal-Oberth e.V., Bonn, 1988
Mathematical Methods in the Applied Sciences, 1986
In this paper, asymptotic expansions with respect to small Reynolds numbers are proved for the sl... more In this paper, asymptotic expansions with respect to small Reynolds numbers are proved for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid past a single plane wall. The flow problem is modelled by a certain boundary value problem for the stationary, nonlinear Navier-Stokes equations. The coefficients of these expansions are the solutions of various, linear Stokes problems which can be constructed by single layer potentials and corresponding boundary integral equations on the boundary surface of the particle. Furthermore, some asymptotic estimates at small Reynolds numbers are presented for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid between two parallel, plane walls and in an infinitely long, rectilinear cylinder of arbitrary cross section. In the case of the flow problem with a single plane wall, the paper is based on a thesis, which the author has written under the guidance of Professor Dr. Wolfgang L. Wendland.
Mathematical Methods in the Applied Sciences, 1989
Error estimates are shown for some spatially discrete Galerkin finite element methods for a non‐l... more Error estimates are shown for some spatially discrete Galerkin finite element methods for a non‐linear heat equation. The approximation schemes studied are based on the introduction of the enthalpy as a new dependent variable, and also on the application of the Kirchhoff transformation and on interpolation of the non‐linear coefficients into standard Lagrangian finite element spaces.
Lecture Notes in Mathematics, 1972
Zeitschrift für die gesamte innere Medizin und ihre Grenzgebiete, 1963
Archiv für experimentelle Veterinärmedizin, 1967
Mathematical Methods in the Applied Sciences, 1982
Data processing is an important tool in airspace surveillance and air traffic control today. In t... more Data processing is an important tool in airspace surveillance and air traffic control today. In this paper the problem is treated how to reconstruct a flown trajectory from its correlated radar plots subject to a certain knowledge of the aircraft manoeuverability and the radar measurement statistics. A variational approach leads to a generalized smoothing spline method. Simulation results are presented. 2 Mathematische Problemstellung Mit Hilfe eines konventionellen Drehradars werden normalenveise zweidimensionale Radardaten zu diskreten Zeitpunkten empfangen, die dann durch
Applicable Analysis, 1979
In this paper we develop a method for the approximation of a broad class of operator equations by... more In this paper we develop a method for the approximation of a broad class of operator equations by reproducing kernels. The relevant operators are defined on Hilbert spaces. Necessary and sufficient conditions for the convergence of the approximation are discussed in detail. The results can be applied-for example-to Fredholm integral operators of the first and second kind and to ordinary and partial differential operators of elliptic type. In this context we refer to [9] for methods to construct reproducing kernels.
Mathematical Methods in the Applied Sciences, 2000
2 collects the dimensionless conservative variables, with the density, v"(v , v)2 the velocity ve... more 2 collects the dimensionless conservative variables, with the density, v"(v , v)2 the velocity vector and e the total energy. The inviscid (Euler) #uxes f G and the viscous terms R G describe the convective and the viscous parts, Coupled Boundary Value Problems 403
Engineering Analysis with Boundary Elements, 1987
Engineering Analysis with Boundary Elements, 1987
Discrete and Continuous Dynamical Systems, 2004
Computing, 1992
The Approximation of Closed Manifolds by Triangulated Manifolds and the Triangulation of Closed M... more The Approximation of Closed Manifolds by Triangulated Manifolds and the Triangulation of Closed Manifolds. Let Fbe a closed surface in ~3. We assume Fis given by the local parameter representation f~:g2~ 3 , i= 1...p, (1.1) as a two-dimensional topological manifold, where f2~ c L~ 2 are open domains of the parameter plane.
Calcolo, 2003
Multidimensional surface potentials associated with elliptic differential operators are defined b... more Multidimensional surface potentials associated with elliptic differential operators are defined by surface integrals involving fundamental solutions of the differential operators which become singular when the observation point approaches the surface. Here we combine the choice of basis functions for the so-called approximate approximation of the surface layer density with the integration of the basis functions over the tangential space by the use of appropriate asymptotic expansions. Our approach leads to cubature formulae involving only nodes of a regular grid. These formulae turn out to be extremely efficient provided the saturation error of the approximate approximation is a priori chosen sufficiently small.
Applicable Analysis, 1979
In this paper we are concerned with the stability of the algebraic multiplicity of eigenvalues of... more In this paper we are concerned with the stability of the algebraic multiplicity of eigenvalues of holomorphic operator-valued functions in the framework of a generalized perturbation theory which is at the same time well-suited for the treatment of approximation methods. It is shown that the algebraic multiplicity of an isolated eigenvalue is stable if the operators under consideration are restricted to the class of so-called approximation-proper families of holomorphic functions of Fredholm mappings acting in certain discrete approximations. As an essential tool in this context the representation formula for the algebraic multiplicity of A. S. Markus and E. I. Sigal is used. The above problem has been rigorously studied in the case when the eigenvalue parameter occurs linearly, but even in this case our result is of interest.
Applicable Analysis, 1985
ABSTRACT