Related papers: Crouzeix-Raviart triangular elements are inf-sup s…
We consider non-conforming discretizations of the stationary Stokes equation in three spatial dimensions by Crouzeix-Raviart type elements. The original definition in the seminal paper by M. Crouzeix and P.-A. Raviart in 1973 is implicit…
In this paper, we prove that Crouzeix-Raviart finite elements of polynomial order $p\geq5$, $p$ odd, are inf-sup stable for the Stokes problem on triangulations. For $p\geq4$, $p$ even, the stability was proved by \'{A}. Baran and G. Stoyan…
In this paper, we consider the discretization of the two-dimensional stationary Stokes equation by Crouzeix-Raviart elements for the velocity of polynomial order $k\geq1$ on conforming triangulations and discontinuous pressure…
The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a…
Most classical finite element schemes for the (Navier-)Stokes equations are neither pressure-robust, nor are they inf-sup stable on general anisotropic triangulations. A lack of pressure-robustness may lead to large velocity errors,…
We prove that the Scott-Vogelius finite elements are inf-sup stable on shape-regular meshes for piecewise quartic velocity fields and higher ($k \ge 4$).
We present a finite element method for Stokes equations using the Crouzeix-Raviart element for the velocity and the continuous linear element for the pressure. We show that the inf-sup condition is satisfied for this pair. Two numerical…
In this paper we will develop a family of non-conforming "Crouzeix-Raviart" type finite elements in three dimensions. They consist of local polynomials of maximal degree $p\in\mathbb{N}$ on simplicial finite element meshes while certain…
We construct several stable finite element pairs for the Stokes problem on barycentric refinements in arbitrary dimensions. A key feature of the spaces is that the divergence maps the discrete velocity space onto the the discrete pressure…
We consider inf-sup stable mixed methods for the time-dependent incompressible Stokes and Navier--Stokes equations, extending earlier work on the steady (Navier-)Stokes Problem. A locking phenomenon is identified for classical inf-sup…
The Scott-Vogelius finite element pair for the numerical discretization of the stationary Stokes equation in 2D is a popular element which is based on a continuous velocity approximation of polynomial order $k$ and a discontinuous pressure…
We present a stable discretization of sea-ice dynamics on triangular grids that can straightforwardly be coupled to an ocean model on a triangular grid with Arakawa C-type staggering. The approach is based on a nonconforming finite element…
We prove that an analog of the Scott-Vogelius finite elements are inf-sup stable on certain nondegenerate meshes for piecewise cubic velocity fields. We also characterize the divergence of the velocity space on such meshes. In addition, we…
In recent years a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are of substantial interest because these discretizations are…
A family of stabilizer-free $P_k$ virtual elements are constructed on triangular meshes. When choosing an accurate and proper interpolation, the stabilizer of the virtual elements can be dropped while the quasi-optimality is kept. The…
This small note proves that the set of triangular numbers is a finitely stable additive basis. This, together with a previous result by the author, shows that triangular numbers and squares are, among all polygonal numbers, the only ones…
In this paper, we propose a discretization for the (nonlinearized) compressible Stokes problem with a linear equation of state $\rho=p$, based on Crouzeix-Raviart elements. The approximation of the momentum balance is obtained by usual…
We construct new Crouzeix-Raviart (CR) spaces of even degree $p$ that are spanned by basis functions mimicking those for the odd degree case. Compared to the standard CR gospel, the present construction allows for the use of nested bases of…
Finite element de Rham complexes and finite element Stokes complexes with various smoothness in three dimensions are systematically constructed. First smooth scalar finite elements in three dimensions are derived through a non-overlapping…
We introduce a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are both piecewise constant (colocated scheme). We use a projection…