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An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element.
- Source :
- Journal of Scientific Computing; Jul2019, Vol. 80 Issue 1, p268-288, 21p
- Publication Year :
- 2019
-
Abstract
- We propose an arbitrary-order discontinuous Galerkin method for second-order elliptic problem on general polygonal mesh with only one degree of freedom per element. This is achieved by locally solving a discrete least-squares over a neighboring element patch. Under a geometrical condition on the element patch, we prove an optimal a priori error estimates in the energy norm and in the L 2 norm. The accuracy and the efficiency of the method up to order six on several polygonal meshes are illustrated by a set of benchmark problems. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08857474
- Volume :
- 80
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Scientific Computing
- Publication Type :
- Academic Journal
- Accession number :
- 136647994
- Full Text :
- https://doi.org/10.1007/s10915-019-00937-y