Anisotropic Wilson element with conforming finite element approximation for a coupled continuum pipe-flow/Darcy model in Karst aquifers

2014 ◽  
Vol 38 (17) ◽  
pp. 4024-4037 ◽  
Author(s):  
Wei Liu ◽  
Qingli Zhao ◽  
Xindong Li ◽  
Jin Li
Keyword(s):  
Finite Element ◽  
Pipe Flow ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Karst Aquifers ◽  
Darcy Model ◽  
Conforming Finite Element ◽  
Wilson Element

scholarly journals ANISOTROPIC QUASI-WILSON ELEMENT WITH CONFORMING FINITE ELEMENT APPROXIMATION FOR COUPLED CONTINUUM PIPE-FLOW/DARCY MODEL IN KARST AQUIFERS

2016 ◽  
Vol 21 (4) ◽  
pp. 431-449 ◽  
Author(s):  
Wei Liu ◽  
Jintao Cui
Keyword(s):  
Finite Element ◽  
Pipe Flow ◽  
Finite Element Approximation ◽  
Flow In Porous Media ◽  
Optimal Error Estimates ◽  
Element Approximation ◽  
Approximation Solution ◽  
Darcy Model ◽  
Conforming Finite Element ◽  
Wilson Element

This paper presents a numerical method for solving systems of partial differential equations describing flow in porous media with an embedded and inclined conduit pipe. This work considers a coupled continuum pipe-flow/Darcy model. The numerical schemes presented are based on combinations of the quasi-Wilson element on anisotropic mesh and the conforming finite element on regular mesh. The existence and uniqueness of the approximation solution are obtained. Optimal error estimates in both L2 and H1 norms are obtained independent of the regularity condition on the mesh. Numerical examples show the accuracy and efficiency of the proposed scheme.

scholarly journals Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow

2020 ◽  
Vol 30 (05) ◽  
pp. 847-865
Author(s):  
Gabriel Barrenechea ◽  
Erik Burman ◽  
Johnny Guzmán
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Inviscid Flow ◽  
Element Approximation ◽  
Well Posedness ◽  
Hodge Laplacian ◽  
Conforming Finite Element ◽  
Velocity Approximation

We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using [Formula: see text](div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the [Formula: see text]-norm of order [Formula: see text]. We also prove error estimates for the pressure error in the [Formula: see text]-norm.

scholarly journals Conforming Finite Element Approximations for a Fourth-Order Steklov Eigenvalue Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Hai Bi ◽  
Shixian Ren ◽  
Yidu Yang
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Fourth Order ◽  
Finite Element Approximation ◽  
Continuous Operator ◽  
Element Approximation ◽  
Morley Element ◽  
Steklov Eigenvalue ◽  
Conforming Finite Element ◽  
Steklov Eigenvalue Problem

This paper characterizes the spectrum of a fourth-order Steklov eigenvalue problem by using the spectral theory of completely continuous operator. The conforming finite element approximation for this problem is analyzed, and the error estimate is given. Finally, the bounds for Steklov eigenvalues on the square domain are provided by Bogner-Fox-Schmit element and Morley element.

NUMERICAL METHODS OF NEW MIXED FINITE ELEMENT SCHEME FOR SINGLE-PHASE COMPRESSIBLE FLOW

2013 ◽  
Vol 11 (01) ◽  
pp. 1350055 ◽  
Author(s):  
SHUYING ZHAI ◽  
XINLONG FENG ◽  
ZHIFENG WENG
Keyword(s):  
Finite Element ◽  
Compressible Flow ◽  
Single Phase ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Optimal Error Estimates ◽  
Element Approximation ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Conforming Finite Element

In this paper, a new mixed finite element scheme is given based on the less regularity of velocity for the single phase compressible flow in practice. Based on the new mixed variational formulation, we give its stable conforming finite element approximation for the P0–P1 pair and its stabilized conforming finite element approximation for the P1–P1 pair. Moreover, optimal error estimates are derived in H1-norm and L2-norm for the approximation of pressure and error estimate in L2-norm for the approximation of velocity by using two methods. Finally, numerical tests confirm the theoretical results of our methods.

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