Journal ArticleDOI
Simple nonconforming quadrilateral Stokes element
Rolf Rannacher,Stefan Turek +1 more
TLDR
In this paper, a simple nonconforming quadrilateral Stokes element based on "rotated" multi-linear shape functions is analyzed, and it is shown that on strongly nonuniform meshes the usual parametric version of this element suffers from a lack of consistency, while its nonparametric counterpart turns out to be convergent with optimal orders.Abstract:
A simple nonconforming quadrilateral Stokes element based on “rotated” multi-linear shape functions is analyzed. On strongly nonuniform meshes the usual parametric version of this element suffers from a lack of consistency, while its nonparametric counterpart turns out to be convergent with optimal orders. This theoretical result is confirmed by numerical tests.read more
Citations
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Book
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
TL;DR: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software.
Numerical Methods For Partial Differential Equations
TL;DR: Numerical methods for partial differential equations is available in the digital library an online access to it is set as public so you can download it instantly and is universally compatible with any devices to read.
Journal ArticleDOI
The nonconforming virtual element method
TL;DR: In this paper, a nonconforming Virtual Element Method (VEM) was proposed for the approximation of second order elliptic problems. But the method is not suitable for finite element methods.
Journal ArticleDOI
A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
TL;DR: A novel stream formulation of the virtual element method (VEM) for the solution of the Stokes problem is proposed and analyzed and it is equivalent to the velocity-pressure (inf-sup stable) mimetic scheme presented.
Journal ArticleDOI
Approximation by quadrilateral finite elements
TL;DR: In this article, the authors consider the approximation properties of finite element spaces on quadrilateral meshes, and demonstrate degradation of the convergence order of these meshes as compared to rectangular meshes for serendipity finite elements and for various mixed and nonconforming finite elements.
References
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Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
BookDOI
Finite element approximation of the Navier-Stokes equations
TL;DR: A mixed finite element method for solving the stokes problem and the time-dependent navier-stokes equations are presented.
Journal ArticleDOI
Multigrid methods for nonconforming finite element methods
D. Braess,R. Verfürth +1 more
TL;DR: A multigrid algorithm for the Crouzeix–Raviart discretization of the Poisson and Stokes equations in two and three dimensions is analyzed for the construction of easily computable $L^2 $-projections based on suitable quadrature rules for the transfer from coarse to fine grids and vice versa.
Journal ArticleDOI
Finite elements for incompressible flow
TL;DR: A finite element method for the solution of viscous incompressible flow problems which incorporates an approximate form of the incompressibility condition automatically into the finite element basis is described.