A discrete divergence free weak Galerkin finite element method for the Stokes equations
[1];
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
- National Science Foundation, Arlington, VA (United States). Division of Mathematical Sciences
- University of Arkansas, Little Rock, AR (United States). Department of Mathematics
- University of Delaware, Newark, DE (United States). Department of Mathematical Sciences
For this research, a discrete divergence free weak Galerkin finite element method is developed for the Stokes equations based on a weak Galerkin (WG) method introduced in [17]. Discrete divergence free bases are constructed explicitly for the lowest order weak Galerkin elements in two and three dimensional spaces. These basis functions can be derived on general meshes of arbitrary shape of polygons and polyhedrons. With the divergence free basis derived, the discrete divergence free WG scheme can eliminate pressure variable from the system and reduces a saddle point problem to a symmetric and positive definite system with many fewer unknowns. Lastly, numerical results are presented to demonstrate the robustness and accuracy of this discrete divergence free WG method.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-00OR22725
- OSTI ID:
- 1415198
- Journal Information:
- Applied Numerical Mathematics, Vol. 125, Issue C; ISSN 0168-9274
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
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