Final Report: Continuous/Discontinuous Variational Multiscale Methods for Variable Density Flows
Abstract
The discontinuous Galerkin (DG) method has found widespread application in elliptic problems with rough coefficients, of which the Darcy flow equations are a prototypical example. One of the long-standing issues of DG approximations is the overall computational cost, and many different strategies have been proposed: the variational multiscale DG method, the hybridizable DG method, the multiscale DG method, the embedded DG method, and the Enriched Galerkin method. We developed a new mixed method, which we named dual-scale Galerkin DG method (DSDG). In the DSDG method, the degrees-of-freedom of a less computationally expensive coarse-scale approximation are linked to the degrees-of-freedom of a base DG approximation. The proposed approach has always similar or improved accuracy with respect to the base DG method, with a considerable reduction in computational cost. We completed an analysis of stability and convergence of the proposed method, in addition to a study on its conservation and consistency properties. Computational tests have confirmed the quality of the DSDG strategy.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 06, 2017
- Accession Number
- AD1063414
Entities
People
- Guglielmo Scovazzi
Organizations
- Duke University