Recovery-Based Error Estimators for Diffusion Problems: Explicit Formulas

We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e., requiring solutions of global problems with mass matrices). In this paper, we develop fully explicit recovery-based error estimators for lower order conforming, mixed, and non- conforming finite element approximations to diffusion problems with full coefficient tensor. When the diffusion coefficient is piecewise constant scalar and its distribution is local quasi-monotone, it is shown theoretically that the estimators developed in this paper are robust with respect to the size of jumps. Numerical experiments are also performed to support the theoretical results

The Impact of Interpretation Problems on Tutorial Dialogue

Supporting natural language input may improve learning in intelligent tutoring systems. However, interpretation errors are unavoidable and require an effective recovery policy. We describe an evaluation of an error recovery policy in the BEE-TLE II tutorial dialogue system and discuss how different types of interpretation problems affect learning gain and user satisfaction. In particular, the problems arising from student use of non-standard terminology appear to have negative consequences. We argue that existing strategies for dealing with terminology problems are insufficient and that improving such strategies is important in future ITS research.

Optimal recovery of integral operators and its applications

In this paper we present the solution to the problem of recovering rather arbitrary integral operator based on incomplete information with error. We apply the main result to obtain optimal methods of recovery and compute the optimal error for the solutions to certain integral equations as well as boundary and initial value problems for various PDE's