Accuracy Control of Computer Simulations and Self-Adaptive Numerical Methods
报告人:Professor Zhiqiang Cai, Purdue University 时间:2019年12月12日15:00
A grand challenge in computer simulations of complex systems is the reliability of computer predictions. A priori error estimates, as provided, e.g., by the standard a priori error analysis for nite element, nite volume, or nite di erence methods, are often insucient since they only yield information on the asymptotic error behavior and require regularity of the solution which are usually not satis ed by complex systems. Self-adaptive numerical methods such as Adaptive Mesh Re nement (AMR) algorithms provide a powerful and automatic approach to scienti c computing. The key ingredient for success of AMR algorithms is a posteriori error estimates that are able to accurately locate sources of global and local error in the current simulation. These considerations clearly show the need for an error estimator that can a posteriori be extracted from the computed numerical solution and the given data of the underlying problem. Such an error estimator is the so-called a posteriori error estimation. This talk will describe basic principles of the a posteriori error estimation techniques and our recent work for nite element approximations to partial di erential equations.