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A Uniformly Stable Nonconforming FEM Based on Weighted Interior Penalties for Darcy-Stokes-Brinkman Equations

Part of: Partial differential equations, boundary value problems Flows in porous media; filtration; seepage

Published online by Cambridge University Press:  20 February 2017

Peiqi Huang  and
Zhilin Li
Peiqi Huang*
Affiliation:
Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
Zhilin Li*
Affiliation:
Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
*
*Corresponding author. Email addresses:pqhuang@njfu.edu.cn (P. Q. Huang), zhilin@math.ncsu.edu (Z. Li)
*Corresponding author. Email addresses:pqhuang@njfu.edu.cn (P. Q. Huang), zhilin@math.ncsu.edu (Z. Li)
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Abstract

A nonconforming rectangular finite element method is proposed to solve a fluid structure interaction problem characterized by the Darcy-Stokes-Brinkman Equation with discontinuous coefficients across the interface of different structures. A uniformly stable mixed finite element together with Nitsche-type matching conditions that automatically adapt to the coupling of different sub-problem combinations are utilized in the discrete algorithm. Compared with other finite element methods in the literature, the new method has some distinguished advantages and features. The Boland-Nicolaides trick is used in proving the inf-sup condition for the multidomain discrete problem. Optimal error estimates are derived for the coupled problem by analyzing the approximation errors and the consistency errors. Numerical examples are also provided to confirm the theoretical results.

Keywords

Fluid structure interactionsDarcy-Stokes-Brinkman equationsStokes equationsDarcy flowdiscontinuous coefficientnonconforming rectangular elementinterior penaltyinf-sup conditionerror estimates

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 76S05: Flows in porous media; filtration; seepage
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 1 , February 2017 , pp. 22 - 43
Copyright
Copyright © Global-Science Press 2017 

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