The Nonconforming Virtual Element Method for a Stationary Stokes Hemivariational Inequality with Slip Boundary Condition

2020 ◽  
Vol 85 (3) ◽  
Author(s):  
Min Ling ◽  
Fei Wang ◽  
Weimin Han
Keyword(s):  
Boundary Condition ◽  
Slip Boundary Condition ◽  
Hemivariational Inequality ◽  
Virtual Element Method ◽  
Slip Boundary ◽  
Virtual Element ◽  
Element Method

scholarly journals Finite element method for a stationary Stokes hemivariational inequality with slip boundary condition

2019 ◽  
Vol 40 (4) ◽  
pp. 2696-2716
Author(s):  
Changjie Fang ◽  
Kenneth Czuprynski ◽  
Weimin Han ◽  
Xiaoliang Cheng ◽  
Xiaoxia Dai
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Directional Derivative ◽  
Slip Boundary Condition ◽  
Hemivariational Inequality ◽  
Slip Boundary ◽  
Element Method

Abstract This paper is devoted to the study of a hemivariational inequality problem for the stationary Stokes equations with a nonlinear slip boundary condition. The hemivariational inequality is formulated with the use of the generalized directional derivative and generalized gradient in the sense of Clarke. We provide an existence and uniqueness result for the hemivariational inequality. Then we apply the finite element method to solve the hemivariational inequality. The incompressibility constraint is treated through a mixed formulation. Error estimates are derived for numerical solutions. Numerical simulation results are reported to illustrate the theoretically predicted convergence orders.

scholarly journals SH wave scattering from 2-D fractures using boundary element method with linear slip boundary condition

2011 ◽  
Vol 188 (1) ◽  
pp. 371-380 ◽  
Author(s):  
Tianrun Chen ◽  
Michael Fehler ◽  
Xinding Fang ◽  
Xuefeng Shang ◽  
Daniel Burns
Keyword(s):  
Boundary Condition ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Wave Scattering ◽  
Slip Boundary Condition ◽  
Sh Wave ◽  
Slip Boundary ◽  
Element Method

scholarly journals SH wave scattering from fractures using boundary element method with linear slip boundary condition

2011 ◽  
Author(s):  
Tianrun Chen ◽  
Michael Fehler ◽  
Xinding Fang ◽  
Xuefeng Shang ◽  
Dan Burns
Keyword(s):  
Boundary Condition ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Wave Scattering ◽  
Slip Boundary Condition ◽  
Sh Wave ◽  
Slip Boundary ◽  
Element Method

scholarly journals Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces

CALCOLO ◽  
2021 ◽  
Vol 58 (3) ◽  
Author(s):  
Elena Bachini ◽  
Gianmarco Manzini ◽  
Mario Putti
Keyword(s):  
Arbitrary Order ◽  
Surface Geometry ◽  
Virtual Element Method ◽  
Anisotropic Character ◽  
Local Reference System ◽  
Local Reference ◽  
Local Parametrization ◽  
Manufactured Solution ◽  
Virtual Element ◽  
Element Method

AbstractWe develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in covariant form using an appropriate local reference system. The knowledge of the local parametrization allows us to consider the two-dimensional VEM scheme, without any explicit approximation of the surface geometry. The theoretical properties of the classical VEM are extended to our framework by taking into consideration the highly anisotropic character of the final discretization. These properties are extensively tested on triangular and polygonal meshes using a manufactured solution. The limitations of the scheme are verified as functions of the regularity of the surface and its approximation.

Non-conforming Harmonic Virtual Element Method: $$h$$ h - and $$p$$ p -Versions

2018 ◽  
Vol 77 (3) ◽  
pp. 1874-1908 ◽  
Author(s):  
Lorenzo Mascotto ◽  
Ilaria Perugia ◽  
Alexander Pichler
Keyword(s):  
Virtual Element Method ◽  
Virtual Element ◽  
Element Method
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