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P1-nonconforming divergence-free finite element method on square meshes for Stokes equations

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.

JEL Classification: 65N30

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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Received: 2019-05-08
Revised: 2019-09-04
Accepted: 2019-09-10
Published Online: 2020-12-11
Published in Print: 2020-12-16

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