Related papers: Exact sequences on Worsey-Farin Splits
We describe a compatible finite element discretisation for the shallow water equations on the rotating sphere, concentrating on integrating consistent upwind stabilisation into the framework. Although the prognostic variables are velocity…
This paper addresses sharpness conditions for constructing $C^r$ conforming finite element spaces from a superspline spaces on general simplicial triangulations. We introduce the concept of extendability for the pre-element spaces, which…
This work is devoted to the high accuracy analysis of a discrete Stokes complex over rectangular meshes with a simple structure. The 0-form in the complex is a non $C^0$ nonconforming element space for biharmonic problems. This plate…
In this study, two-dimensional finite element complexes with various levels of smoothness, including the de Rham complex, the curldiv complex, the elasticity complex, and the divdiv complex, are systematically constructed. Smooth scalar…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
We consider a sharp interface formulation for the multi-phase Mullins-Sekerka flow. The flow is characterized by a network of curves evolving such that the total surface energy of the curves is reduced, while the areas of the enclosed…
Numerical simulation of incompressible viscous flow, in particular in three space dimensions, continues to remain a challenging task. Space-time finite element methods feature the natural construction of higher order discretization schemes.…
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…
We introduce an efficient split finite element (FE) discretization of a y-independent (slice) model of the rotating shallow water equations. The study of this slice model provides insight towards developing schemes for the full 2D case.…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
Let $S$ be a complete flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components of the space of all curves on $S$ which start and end at given points in given directions, and whose curvatures…
In this paper, we first construct a nonconforming finite element pair for the incompressible Stokes problem on quadrilateral grids, and then construct a discrete Stokes complex associated with that finite element pair. The finite element…
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 show that the Ramsey theory of block sequences in infinite-dimensional discrete vector spaces can be parametrized by perfect sets. As special cases, we prove combinatorial dichotomies for definable families of partitions and linear…
We study stochastic Navier-Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a…
A finite element cochain complex on Cartesian meshes of any dimension based on the H1-inner product is introduced. It yields H1-conforming finite element spaces with exterior derivatives in H1. We use a tensor product construction to obtain…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
In this paper, we construct and analyze divergence-free finite element methods for the Stokes problem on smooth domains. The discrete spaces are based on the Scott-Vogelius finite element pair of arbitrary polynomial degree greater than…
We construct and analyze a CutFEM discretization for the Stokes problem based on the Scott-Vogelius pair. The discrete piecewise polynomial spaces are defined on macro-element triangulations which are not fitted to the smooth physical…
We develop two unfitted finite element methods for the Stokes equations using $H^{\text{div}}$-conforming finite elements. Both methods achieve optimal convergence for velocity, ensure pointwise divergence-free velocity fields, and produce…