期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 54, 期 6, 页码 3411-3435出版社
SIAM PUBLICATIONS
DOI: 10.1137/15M1049531
关键词
virtual element method; finite element method; polygonal and polyehdral mesh; high-order discretization; Stokes equations
资金
- Engineering and Physical Sciences Research Council of the United Kingdom [EP/L022745/1]
- Laboratory Directed Research and Development program (LDRD), U.S. Department of Energy Office of Science, Office of Fusion Energy Sciences, under National Nuclear Security Administration of the U.S. Department of Energy by Los Alamos National Laboratory [DE-AC52-06NA25396]
- EPSRC [EP/L022745/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/L022745/1] Funding Source: researchfish
We present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non polynomial functions is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据