PNNL

Abstract

In recent work we have shown how an accurate reduced model can be utilized to perform mesh renement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity from the large to the small scales of the solution. Since this is not always available, we present in the current work a framework which shares the merits and basic idea of the previous approach but does not require an explicit knowledge of a reduced model. Moreover, the current framework can be applied for renement in both random and physical space. In this manuscript we focus on the application to random space mesh renement. We study examples of increasing difficulty (from ordinary to partial differential equations) which demonstrate the effciency and versatility of our approach. We also provide some results from the application of the new framework to physical space mesh refinement.