P1-nonconforming divergence-free finite element method on square meshes for Stokes equations
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Chunjae Park
Abstract
Recently, the P1-nonconforming finite element space over square meshes has been proved stable to solve Stokes equations with the piecewise constant space for velocity and pressure, respectively. In this paper, we will introduce its locally divergence-free subspace to solve the elliptic problem for the velocity only decoupled from the Stokes equation. The concerning system of linear equations is much smaller compared to the Stokes equations. Furthermore, it is split into two smaller ones. After solving the velocity first, the pressure in the Stokes problem can be obtained by an explicit method very rapidly.
Funding source: National Research Foundation of Korea (NRF)
Funding source: Ministry of Education, Science and Technology
Award Identifier / Grant number: NRF-2017R1D1A1A02019336
Funding statement: The present research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2017R1D1A1A02019336).
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations
- Coupling of virtual element and boundary element methods for the solution of acoustic scattering problems
- P1-nonconforming divergence-free finite element method on square meshes for Stokes equations
Artikel in diesem Heft
- Frontmatter
- Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations
- Coupling of virtual element and boundary element methods for the solution of acoustic scattering problems
- P1-nonconforming divergence-free finite element method on square meshes for Stokes equations
