Related papers: An arbitrary-order discrete de Rham complex on pol…
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…
We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $\Omega\subset\mathbb{R}^2$, possibly occupied by piecewise homogeneous media with different propagation speeds.…
We present new finite elements for solving the Riesz maps of the de Rham complex on triangular and tetrahedral meshes at high order. The finite elements discretize the same spaces as usual, but with different basis functions, so that the…
The present paper is a continuation of our work on curved finitary spacetime sheaves of incidence algebras and treats the latter along Cech cohomological lines. In particular, we entertain the possibility of constructing a non-trivial de…
This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…
We show that, given a projective regular function f on a smooth quasi-projective variety over C, the corresponding cohomology groups of the algebraic de Rham complex with twisted differential d-df and of the complex of algebraic forms with…
In this present paper we consider a full divergence-free of high order virtual finite element algorithm to approximate the stationary inductionless magnetohydrodynamic model on polygonal meshes. More precisely, we choice appropriate virtual…
We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…
The recent results of An, Luan, and Yen [Differential stability in convex optimization via generalized polyhedrality. Vietnam J. Math. https://-doi.org/10.1007/s10013-024-00721-y] on differential stability of parametric optimization…
We extend the results of Deligne and Illusie on liftings modulo $p^2$ and decompositions of the de Rham complex in several ways. We show that for a smooth scheme $X$ over a perfect field $k$ of characteristic $p>0$, the truncations of the…
In this work we construct a low-order nonconforming approximation method for linear elasticity problems supporting general meshes and valid in two and three space dimensions. The method is obtained by hacking the Hybrid High-Order method,…
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
In this work we address the problem of finding serendipity versions of approximate de Rham complexes with enhanced regularity. The starting point is a new abstract construction of general scope which, given three complexes linked by…
We derive explicit a priori consistency error estimates for a standard finite element discretization of the Poisson equation on convex domains, where the domain is approximated by an internal convex polyhedron. The obtained explicit…
In this article we develop a fully discrete variational scheme that approximates the equations of three dimensional elastodynamics with polyconvex stored energy. The fully discrete scheme is based on a time-discrete variational scheme…
We propose an arbitrarily higher (even) order implicit leapfrog scheme for time discretization of a three-field formulation of Maxwell's equations. We use this in conjunction with an arbitrarily higher-order and compatible discretization…
In this paper, we study the L2 stability of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider the case when a small periodic perturbation is applied to a uniform mesh. For this case, we…
Polynomial stability of exact solution and modified truncated Euler-Maruyama method for stochastic differential equations with time-dependent delay are investigated in this paper. By using the well known discrete semimartingale convergence…
We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal…