Johannes Kepler Symposium für Mathematik

Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird Prof. Martin J. Gander, Section de Mathématiques, Université de Genève, am Fri, Aug. 5, 2011 um 10:30 Uhr im HS 13 einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "Euler, Lagrange, Ritz, Galerkin, Courant, Clough: On the Road to the Finite Element Method" halten, zu dem die Veranstalter des Symposiums,

O.Univ.-Prof. Dr. Ulrich Langer,
Univ.-Prof. Dr. Gerhard Larcher
A.Univ.-Prof. Dr. Jürgen Maaß, und
die ÖMG (Österreichische Mathematische Gesellschaft)

hiermit herzlich einladen.

Series A - General Colloquium:

The intention is to present general information not only to experts, but also to students and guests from outside the mathematical institutes.

Euler, Lagrange, Ritz, Galerkin, Courant, Clough: On the Road to the Finite Element Method

The so-called Ritz-Galerkin method is one of the most fundamental tools of modern computing. Its origins lie in the variational calculus of Euler-Lagrange and in the thesis of Walther Ritz, who died just over 100 years ago at the age of 31 after a long struggle against tuberculosis. The thesis was submitted in 1902 in Goettingen, in a period of dramatic developments in Physics. Ritz tried to explain the phenomenon of Balmer series in spectroscopy using eigenvalue problems of partial differential equations on rectangular domains. While this physics of the model quickly turned out to be completely obsolete, his mathematics enabled him later to solve difficult problems in applied sciences. He thereby revolutionized the variational calculus and became one of the fathers of modern computational mathematics.

The Ritz method was immediately recognized by Russian mathematicians as a fundamental contribution, and put to use in the computational simulation of beams and plates, which led to the seminal paper of Galerkin in 1915. In Europe however, especially in the mathematical center of that time in Goettingen, it received very little attention, even though Ritz obtained a price from the French Academy of Sciences, after having lost in the official competition for the Vaillant price in 1907 to Hadamard. It was only during the second world war, long after Ritz's death, in an address of Courant in front of the AMS, that the potential of Ritz's invention was fully recognized, and Courant presented what we now call the finite element method. This name was given to the method after Clough reinvented it in a seminal paper, working for Boeing.

We will see in this talk that the path leading to modern computational methods and theory was a long struggle over three centuries requiring the efforts of many great mathematicians.