Back to Search
Start Over
A primal-dual finite element method for first-order transport problems.
- Source :
-
Journal of Computational Physics . Sep2020, Vol. 417, pN.PAG-N.PAG. 1p. - Publication Year :
- 2020
-
Abstract
- • This numerical scheme is devised by the primal-dual weak Galerkin(PDWG) framework. • The PDWG method can be interpreted as a constraint optimization process. • The PDWG scheme conserves mass locally on each element. • Optimal order error estimates are derived for the PDWG solution. This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific computing. The PD-WG method is based on a variational formulation of the modeling equation for which the differential operator is applied to the test function so that low regularity for the exact solution of the original equation is sufficient for computation. The PD-WG finite element method indeed yields a symmetric system involving both the original equation for the primal variable and its dual for the dual variable (also known as Lagrangian multiplier). For the linear transport problem, it is shown that the PD-WG method offers numerical solutions that conserve mass locally on each element. Optimal order error estimates in various norms are derived for the numerical solutions arising from the PD-WG method with weak regularity assumptions on the modelling equations. A variety of numerical results are presented to demonstrate the accuracy and stability of the new method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00219991
- Volume :
- 417
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Physics
- Publication Type :
- Academic Journal
- Accession number :
- 143682061
- Full Text :
- https://doi.org/10.1016/j.jcp.2020.109571