Related papers: The enriched Crouzeix-Raviart elements are equival…
For the Crouzeix-Raviart and enriched Crouzeix-Raviart elements, asymptotic expansions of eigenvalues of the Stokes operator are derived by establishing two pseudostress interpolations, which admit a full one-order supercloseness with…
We investigate the piecewise linear nonconforming Crouzeix-Raviar and the lowest order Raviart-Thomas finite-element methods for the Poisson problem on three-dimensional anisotropic meshes. We first give error estimates of the…
In this paper, a new method is proposed to prove the superconvergence of both the Crouzeix-Raviart and Morley elements. The main idea is to fully employ equivalences with the first order Raviart-Thomas element and the first order…
In this work, we fully explore three refined convergence structures of the lowest-order rectangular Raviart-Thomas element in solving the Laplace eigenvalue problem. Firstly, the scheme possesses a property of supercloseness between the…
In this paper we propose a penalized Crouzeix-Raviart element method for eigenvalue problems of second order elliptic operators. The key idea is to add a penalty term to tune the local approximation property and the global continuity…
Asymptotic expansions are derived for eigenvalues produced by both the Crouzeix-Raviart element and the enriched Crouzeix--Raviart element. The expansions are optimal in the sense that extrapolation eigenvalues based on them admit a fourth…
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, an improved superconvergence analysis is presented for both the Crouzeix-Raviart element and the Morley element. The main idea of the analysis is to employ a discrete Helmholtz decomposition of the difference between the…
We studied an anisotropic modified Crouzeix--Raviart finite element method for the rotational form of a stationary incompressible Navier--Stokes equation with large irrotational body forces. We present an anisotropic $H^1$ error estimate…
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,…
In this paper, we propose and analyze an adaptive Crouzeix-Raviart finite element method for computing the first Dirichlet eigenpair of the $p$-Laplacian problem. We prove that the sequence of error estimators produced by the adaptive…
In this paper, three high-accuracy methods for eigenvalues of second order elliptic operators are proposed by using the nonconforming Crouzeix-Raviart(CR for short) element and the nonconforming enriched Crouzeix-Raviart(ECR for short)…
Under some regularity assumptions, we report an a priori error analysis of a dG scheme for the Poisson and Stokes flow problem in their dual mixed formulation. Both formulations satisfy a Babu\v{s}ka-Brezzi type condition within the space…
We present first-order nonconforming Crouzeix-Raviart discretizations for the nonlinear generalized Stokes equations with $(r,\epsilon)$-structure. Thereby the velocity-errors are independent of the pressure-error; i.e., the method is…
Electrokinetic phenomena in nanopore sensors and microfluidic devices require accurate simulation of coupled fluid-electrostatic interactions in geometrically complex domains with irregular boundaries and adaptive mesh refinement. We…
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…
We discuss the error analysis of the lowest degree Crouzeix-Raviart and Raviart-Thomas finite element methods applied to a two-dimensional Poisson equation. To obtain error estimations, we use the techniques developed by Babu\v{s}ka-Aziz…
We show that, using the Crouzeix-Raviart scheme, a cheap algebraic transformation, applied to the coupled velocity-pressure linear systems issued from the transient or steady Stokes or Navier-Stokes problems, leads to a linear system only…
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…
In arXiv:2307.03503 [math.NA] we commenced to study a variant of the Raviart-Thomas mixed finite element method for triangles, to solve second order elliptic equations in a curved domain with Neumann or mixed boundary conditions. It is well…