Adaptive Modelling and Discretization Error Control (21w5214)

Organizers

(University of Zurich)

Mark Ainsworth (Brown University)

(Simon Fraser University)

Ricardo Nochetto (University of Maryland)

Description

The Banff International Research Station will host the "Adaptive Modelling and Discretization Error Control" workshop in Banff from January 17 to January 22, 2021.


Whether we cross over a bridge, board the latest aircraft to go on holiday, or receive medical treatment using nano-technology, we are relying on predictions and design decisions that are increasingly based on the results of computer simulation. While the layman cannot help but be impressed by these modern day developments, it is nonetheless true that the results of computer simulation can only ever be approximately correct and are subject to many sources of uncertainty and inaccuracies that can, if not properly understood, mean that the bridge or aircraft or medical treatment is based on flawed information.

Uncertainty and inaccuracy arises from the facts that a) these computer simulations involve the solution of complicated mathematical equations: partial differential equations and integral equations and b) the result of the simulation is only an approximation of the physical phenomenon where the quality of approximation depends on the accuarcy of the data measurements, the chosen model (e.g. the decision whether one has to take into account shear winds for the construction of a bridge or whether this effect is negligible) and the precision how the final equations are solved.

Hence, it is of utmost importance not only to carry out the simulation but also to compute its accuracy, i.e., the "error bars" as the physists are naming it, by an additional computation. This step involves deep mathematics and is called "a posteriori error control". The computer simulation together with the a posteriori error bounds finally make a simulation result reliable and ready for practical applications and decision.

It is the goal of this workshop to bring together the leading experts in various fields of a posteriori error control to create synergies for combining the separated know-how towards the ultimate goal of efficient and reliable modelling of complex physical phenomena and real-world applications.


The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).