Bücher der Reihe International Series of Numerical Mathematics

The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. An appreciation of his li fe and contributions was presented verbally by Georges Alexits, while the written version bears the signa tures of both Alexits and Marc Zamansky.

About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990.

Numerical simulation and modelling of electric circuits and semiconductor devices are of primal interest in today's high technology industries. They include contributions on special topics of current interest in circuit and device simulation, as well as contributions that present an overview of the field.

These Proceedings include 42 of the 49 invited conference papers, three papers sub mitted subsequently, and a report devoted to new and unsolved problems based on two special problem sessions and as augmented by later communications from the participants.

Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications.

It takes an intermediate position between elliptic and parabolic inequalities and comprises an elliptic differential operator, a memory term and time-dependent convex constraint sets.

These proceedings contain a selection of papers presented at the Third European Conference on Multigrid Methods which was held in Bonn on October 1-4, 1990. The field of parallel Multigrid variants, having been started at the second European Multigrid Conference, is now at the centre of interest.

persönlichen Kontakt der Wissenschaftler untereinander zustande kommt, als die unpersönliche, nur literarische Information.

Whilst improperly posed problems appear in several branches of applied and pure mathematics, this conference concentrated mainly on the practical treatment of ill­ posedness. The participants came from 12 countries. The interchange of ideas reflected the spectrum of questions arising in connection with the subject of the conference, where currently progresses in research are made. This volume contains 17 papers presented at the con­ ference. Focal points in the programme were: Problems of regularisation, parameter identification, free boundary and inverse problems in differential equations and inte­ gral equations of the first kind. Problems, which appear in science, in technical fields and in medicine are dis­ cussed as well as general operator equations. In a jOint discussion, several open problems have been worked out which are collected at the end of the volume. The editor's thanks go to all contributors and parti­ cipants who made the conference a success; to the manage­ ment of the institute with its unique atmosphere; to the Birkhauser Verlag for the possibility to publish the vo­ lume in the well-known ISNM series; to Dr. P. Jochum (Mlin­ chen) for assistance in organization and to Mrs. Chr. Rogg (Augsburg) for her excellent typing of several manuscripts.

This volume contains contributions from international experts in the fields of constructive approximation. This area has reached out to encompass the computational and approximation-theoretical aspects of various interesting fields in applied mathematics.

The International Meetings on Approximation Theory attempt to keep track in particular of fun damental advances in the theory of function approximation, for example by (or thogonal) polynomials, (weighted) interpolation, multivariate quasi-interpolation, splines, radial basis functions and several others.

It addresses classical inequalities related to means or to convexity as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities occurring in geometrical contexts.

The topics treated cover different problems on multivariate approximation such as polynomial approximation on simplices, multivariate splines (box-splines, dimension of spline spaces), blending methods, multivariate Hermite interpolation, data smoothing and surface representation, and multivariate summation methods.

O I 1 -1 durch die GauB-Quadraturformel Q I n n L w 0 f (x 0) ¿ i=1 1 1 Sei Rn : = I - Q das Fehlerfunktional. n Izl1, Fur eine im Kreis Kr I Kr : = {z E a: holomorphe Funktion f, f(z) = L i=O sei f i i ¿ = x . ( 1. 1) : = sup{ I a 0 I r i E:JN und R (qo) * O}, qo (x) o 1 n 1 1 In Xr := {f: f holomorph in Kr und Iflr < oo} ist I . I eine Seminorm. Das Fehlerfunktional Rn ist in r (X I· I r) stetig I und fUr II Rn II I r, gilt die Identitat 00 (1 . 2) L i=O Dieser Zugang zu ableitungsfreien Abschatzungen des Fehlerterms (1 ¿ 3) geht auf Hammerlin [4] zurUck. 15 Erftillt die Gewichtsfunktion w eine der Bedingungen w (t ) w(t ) 1 2 ;;; (1. 4. a) w (-t ) w (-t ) 1 2 beziehungsweise w (t ) w(t ) 1 2 (1. 4. b) ~ w (-t ) w (-t ) 1 2 so gilt mit P (x) (X-X ) ¿. ¿ (X-X ) ftir die Fehlernorm 1 n n r 1 Pn(x) (1. 5. a) --,-. . - J w (x) dx Pn(r) -1 r-x beziehungsweise r 1 P (x) (1. 5. b) ( ) J w(x) ~ dx .

This volume contains a collection of 23 papers presented at the 4th French-German Conference on Optimization, hold at Irsee, April 21 - 26, 1986. The scientifique program consisted of four survey lectures of a more tutorical character and of 61 contributed papers covering almost all areas of optimization.

This monograph collects research and expository articles reflect­ ing the interaction and the cooperation of different groups in several European institut ions concerning current research on mathematical models for the behaviour of materials with phase change. These papers were presented and discussed in a Workshop held at Obidos, Portugal, du ring the first three days of October, 1988, and grew out of a two year period of intensive exploitation of differ­ ent abilities and mathematical experiences of the six participating groups, namely, in the University of Augsburg, wh ich was the co­ ordination center of this project, the Laboratoire Central des Ponts et Chaussees of Paris, the Aristoteles University of Thessaloniki, the University of Florence, the University of Lisbon and the University of Oxford. This project was carried out under the title "Mathemat­ ical Models of Phase Transitions and Numerical Simulation" , in the framework of twinning program for stimulation of cooperation and scientific interchange, sponsored by the European Community. The underlying idea of the project was to create and study the mathematical models arising in applied engineering problems with free boundaries in a broad sense, namely in melting and freezing problems, diffusion-reaction processes, solid-solid phase transition, hysteresis phenomena, "mushy region" descriptions, contact prob­ lems with friction andjor adhesion, elastoplastic deformations, etc. vi This large spectrum of applied problems have in common the main feature of brusque transitions of their qualitative behaviour that correspond, in general, to non-classical discontinuous monotone or non monotone strong nonlinearities in the mathematical equations.

This book contains the refereed papers which were presented at the interna tional conference on "Multivariate Approximation and Splines" held in Mannheim, Germany, on September 7-10,1996.

This volume contains a collection of papers dealing with applications of orthogonal polynomials and methods for their computation, of interest to a wide audience of numerical analysts, engineers, and scientists. The applications address problems in applied mathematics as well as problems in engineering and the sciences.

A collection of papers by international contributors describing new developments in the fields of univariate and multivariate approximation theory. This research has applications in areas such as computer-aided geometric design, as applied in engineering and medical technology (e.g. computerized tomography).

For this pur pose, the technical committee Mathematics of Control of IFAC organizes biennial conferences with the objective of bringing together experts to exchange ideas, ex periences and future developments in control applications of optimization.

While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have become a major tool in numerical analysis of partial differential equations.

Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed.This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems.Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.