This talk will discuss a substantial interplay of algebraic topology with numerical analysis which has developed over the last decade. During this period, de Rham cohomology and the Hodge theory of Riemannian manifolds have come to play a crucial role in the development and understanding of computational algorithms for the solution of problems i...
Creator:
Arnold, Douglas N. (University of Minnesota, Twin Cities)
Created:
2013-10-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The puzzling and important phenonenon of wave localization arises in many physical and mathematical contexts, with applications range from the quantum mechanics of electrical conduction through the design of optical devices to the construction of noise abatement systems, to name but a few. Although studied by physicists and mathematicians for th...
Creator:
Arnold, Douglas N. (University of Minnesota, Twin Cities)
Created:
2017-03-08
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The finite element exterior calculus, FEEC, has provided aviewpoint from which to understand and develop stable finiteelement methods for a variety of problems. It has enabled us tounify, clarify, and refine many of the classical mixed finiteelement methods, and has enabled the development of previouslyelusive stable mixed finite elements for el...
Creator:
Arnold, Douglas N. (University of Minnesota, Twin Cities)
Created:
2010-11-01
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.