相关论文: Partially discontinuous nodal finite elements for …

The Hilbert spaces $H(\mathrm{curl})$ and $H(\mathrm{div})$ are needed for variational problems formulated in the context of the de Rham complex in order to guarantee well-posedness. Consequently, the construction of conforming subspaces is…

We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogous of the normal derivative…

In this paper, we propose a family of nonconforming finite elements for $2m$-th order partial differential equations in $\mathbb{R}^n$ on simplicial grids when $m=n+1$. This family of nonconforming elements naturally extends the elements…

We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…

The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…

This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element…

We provide a finite element discretization of $\ell$-form-valued $k$-forms on triangulation in $\mathbb{R}^{n}$ for general $k$, $\ell$ and $n$ and any polynomial degree. The construction generalizes finite element Whitney forms for the…

In this paper we present a unified framework for constructing spectrally equivalent low-order-refined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in $H^1$, $H({\rm curl})$, and…

In this work we study various continuous finite element discretization for two dimensional hyperbolic partial differential equations, varying the polynomial space (Lagrangian on equispaced, Lagrangian on quadrature points (Cubature) and…

We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…

We introduce the concept of half-closed nodes for nodal discontinuous Galerkin (DG) discretisations. Unlike more commonly used closed nodes in DG, where on every element nodes are placed on all of its boundaries, half-closed nodes only…

Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…

A new $H(\textrm{divdiv})$-conforming finite element is presented, which avoids the need for super-smoothness by redistributing the degrees of freedom to edges and faces. This leads to a hybridizable mixed method with superconvergence for…

Based on the Stokes complex with vanishing boundary conditions and its dual complex, we reinterpret a grad-curl problem arising from the quad-curl problem as a new vector potential formulation of the three-dimensional Stokes system. By…

With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high…

We study several numerical discretization techniques for the one-space plus one-time dimensional Dirac equation, including finite difference and space-time finite element methods. Two finite difference schemes and several space-time finite…

The existence of uniformly bounded discrete extension operators is established for conforming Raviart-Thomas and N\'ed\'elec discretisations of $H(div)$ and $H(curl)$ on locally refined partitions of a polyhedral domain into tetrahedra.

This paper introduces a Sobolev-like space of order $3/2$, denoted as $\widehat{H}^{3/2}$, for Lagrangian finite elements, especially for $C^0$ elements. It is motivated by the limitations of current stability analysis of the evolving…

In this work we present a consistent reduction of the relaxed micromorphic model to its corresponding two-dimensional planar model, such that its capacity to capture discontinuous dilatation fields is preserved. As a direct consequence of…

A linear evolving surface partial differential equation is first discretized in space by an arbitrary Lagrangian Eulerian (ALE) evolving surface finite element method, and then in time either by a Runge-Kutta method, or by a backward…