Space-time GMsFEM for transport equations Academic Article uri icon

abstract

  • 2018, Springer-Verlag GmbH Germany, part of Springer Nature. In this paper, we propose a space-time GMsFEM for transport equations. Most of existing multiscale approaches use spatial multiscale basis functions or upscaling, and there are very few works that design space-time multiscale functions to solve the transport equation on a coarse grid. For the time dependent problems, the use of space-time multiscale basis functions offers several advantages as the spatial and temporal scales are intrinsically coupled. By using the GMsFEM idea with a space-time framework, one obtains a better dimensional reduction taking into account features of the solutions in both space and time. In addition, the time-stepping can be performed using much coarser time step sizes compared to the case when spatial multiscale basis are used. Our scheme is based on space-time snapshot spaces and model reduction using space-time spectral problems derived from the analysis. We give the analysis for the well-posedness and the spectral convergence of our method. We also present some numerical examples to demonstrate the performance of the method. In all examples, we observe a good accuracy with a few basis functions.

published proceedings

  • GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS

author list (cited authors)

  • Chung, E. T., Efendiev, Y., & Li, Y.

citation count

  • 1

complete list of authors

  • Chung, Eric T||Efendiev, Yalchin||Li, Yanbo

publication date

  • November 2018