Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions
arXiv:1312.4223 · doi:10.1007/978-3-319-06898-5_12
Abstract
We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.
19 pages, 7 figures
References in corpus (3)
- Finite element exterior calculus: from Hodge theory to numerical stability
- An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary
- Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions