相关论文: Fully discrete polynomial de Rham sequences of arb…

We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…

Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…

In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…

In this paper we develop an evolution of the $C^1$ virtual elements of minimal degree for the approximation of the Cahn-Hilliard equation. The proposed method has the advantage of being conforming in $H^2$ and making use of a very simple…

We propose a new fictitious domain finite element method, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the boundary. To impose the Dirichlet boundary conditions, we…

We study the use of polyhedral discretizations for the solution of heat diffusion and elastodynamic problems in computer graphics. Polyhedral meshes are more natural for certain applications than pure triangular or quadrilateral meshes,…

In a classical case, orthogonal polynomial sequences are in such a way that the $ n $th polynomial has the exact degree $n$. Such sequences are complete and form a basis of the space for any arbitrary polynomial. In this paper, we introduce…

We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.

Compatible schemes localize degrees of freedom according to the physical nature of the underlying fields and operate a clear distinction between topological laws and closure relations. For elliptic problems, the cornerstone in the scheme…

We introduce the "sharp" (universal) extension of a 1-motive (with additive factors and torsion) over a field of characteristic zero. We define the "sharp de Rham realization" by passing to the Lie-algebra. Over the complex numbers we then…

Equal-volume polygons are obtained from adequate discretizations of curves in 3-space, contained or not in surfaces. In this paper we explore the similarities of these polygons with the affine arc-length parameterized smooth curves to…

The accurate and efficient representation of atmospheric dynamics remains a central challenge in numerical weather prediction. A particular difficulty arises from the strong anisotropy of the atmosphere, in which horizontal and vertical…

In this work we develop a discrete trace theory that spans non-conforming hybrid discretization methods and holds on polytopal meshes. A notion of a discrete trace seminorm is defined, and trace and lifting results with respect to a…

We introduce the concept of data-driven finite element methods. These are finite-element discretizations of partial differential equations (PDEs) that resolve quantities of interest with striking accuracy, regardless of the underlying mesh…

A new kind of spline geometric method approach is presented. Its main ingredient is the use of well established spline spaces forming a discrete de Rham complex to construct a primal sequence $\{X^k_h\}^n_{k=0}$, starting from splines of…

This paper proposes a construction of $C^r$ conforming finite element spaces with arbitrary $r$ in any dimension. It is shown that if $k \ge 2^{d}r+1$ the space $\mathcal P_k$ of polynomials of degree $\le k$ can be taken as the shape…

This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…

In this paper, we propose a fully discrete mixed finite element method for solving the time-dependent Ginzburg--Landau equations, and prove the convergence of the finite element solutions in general curved polyhedra, possibly nonconvex and…

We investigate discretization of $H(\mathrm{curl})$ and $H(\mathrm{div})$ in two and three space dimensions by partially discontinuous nodal finite elements, i.e., vector-valued Lagrange finite elements with discontinuity in certain…

Certain energy-conservative Galerkin discretizations for nonlinear dispersive wave equations have revealed an unusual convergence behavior: optimal convergence is attained when continuous Lagrange finite element spaces of odd polynomial…