Related papers: Analysis of a combined NC1-C2 method for elliptic …
We consider the lowest--degree nonconforming finite element methods for the approximation of elliptic problems in high dimensions. The $P_1$--nonconforming polyhedral finite element is introduced for any high dimension. Our finite element…
We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…
We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional.…
We study some numerical methods for solving second order elliptic problem with interface. We introduce an immersed interface finite element method based on the `broken' $P_1$-nonconforming piecewise linear polynomials on interface…
In this work we present a generic framework for non-conforming finite elements on polytopal meshes, characterised by elements that can be generic polygons/polyhedra. We first present the functional framework on the example of a linear…
A nonconforming $P_2$ finite element is constructed by enriching the conforming $P_2$ finite element space with seven $P_2$ nonconforming bubble functions (out of fifteen such bubble functions on each tetrahedron). This spacial…
In this paper, we propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of the new finite element…
A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…
This work introduces two 11-node triangular prism elements for 3D elliptic problems. The degrees of freedom (DoFs) of both elements are at the vertices and face centroids of a prism cell. The first element is $H^1$-nonconforming and works…
In this paper, two nonconforming finite element schemes that use piecewise cubic and piecewise quartic polynomials respectively are constructed for the planar biharmonic equation with optimal convergence rates on general shape-regular…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
This work proposes two nodal type nonconforming finite elements over convex quadrilaterals, which are parts of a finite element exact sequence. Both elements are of 12 degrees of freedom (DoFs) with polynomial shape function spaces…
This paper presents a nonconforming finite element scheme for the planar biharmonic equation which applis piecewise cubic polynomials ($P_3$) and possesses $\mathcal{O}(h^2)$ convergence rate in energy norm on general shape-regular…
A mixed finite element method combining an iso-parametric $Q_2$-$P_1$ element and an iso-parametric $P_2^+$-$P_1$ element is developed for the computation of multiple cavities in incompressible nonlinear elasticity. The method is…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
In this paper, we introduce new stable mixed finite elements of any order on polytopal mesh for solving second order elliptic problem. We establish optimal order error estimates for velocity and super convergence for pressure. Numerical…
In this article, a family of $H^2$-nonconforming finite elements on tetrahedral grids is constructed for solving the biharmonic equation in 3D. In the family, the $P_\ell$ polynomial space is enriched by some high order polynomials for all…
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be…
A nonconforming $P_3$ finite element is constructed by enriching the conforming $P_3$ finite element space with three $P_3$ nonconforming bubbles and six additional $P_4$ nonconforming bubbles, on each tetrahedron. Here the divergence of…