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The finite-element method is a preferred numerical method when electromagnetic fields at high accuracy are to be computed in nano-optics design. Here, we demonstrate a finite-element method using hp-adaptivity on tetrahedral meshes for…

We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger--Reissner mixed…

Numerical Analysis · Mathematics 2014-01-29 Douglas N. Arnold , Gerard Awanou , Ragnar Winther

A robust nonconforming mixed finite element method is developed for a strain gradient elasticity (SGE) model. In two and three dimensional cases, a lower order $C^0$-continuous $H^2$-nonconforming finite element is constructed for the…

Numerical Analysis · Mathematics 2023-09-25 Mingqing Chen , Jianguo Huang , Xuehai Huang

The properties of the spaces of Sugeno integrable functions are quite different from those of the ordinary spaces of Lebesgue integrable functions. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces, in…

Classical Analysis and ODEs · Mathematics 2022-08-23 Jun Kawabe

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…

Numerical Analysis · Mathematics 2025-07-23 Kaibo Hu , Ting Lin

The theory of spaces with different (not only by sign) contravariant and covariant affine connections and metrics [}$(\bar{L}_n,g)$\QTR{it}{-spaces] is worked out within the framework of the tensor analysis over differentiable manifolds and…

General Relativity and Quantum Cosmology · Physics 2007-05-23 S. Manoff

Extending the `metric spaces' of Lawvere, we study `real metrics', with values in the extended real line. Formally, this ordered set is a symmetric monoidal closed category, and our structures are enriched categories on the latter.…

Algebraic Topology · Mathematics 2026-05-14 Marco Grandis

This article introduces a novel approach for broken-FEEC (Finite Element Exterior Calculus), extending its application to locally refined spline spaces with non-matching interfaces. Traditional broken-FEEC allows for discontinuous…

Numerical Analysis · Mathematics 2025-12-01 Martin Campos Pinto , Frederik Schnack

We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…

Numerical Analysis · Mathematics 2021-01-26 Erik Burman , Peter Hansbo , Mats G. Larson

We develop a continued fraction algorithm in finite extensions of $\Q_p$ generalising certain algorithms in $\Q_p$, and prove the finiteness property for certain small degree extensions. We also discuss the metrical properties of the…

Number Theory · Mathematics 2024-07-08 Manoj Choudhuri , Prashant J. Makadiya

We characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator, together with estimates of the norm of such an operator. This result is used to the study of strengthenings…

Functional Analysis · Mathematics 2012-10-23 Wieslaw Kubiś , Ondrej Kalenda

(This is a report for the Proceedings of ``Journees Relativistes 1993'' written in September 1993. Containes a short description of the results published elsewhere in the joint paper with A. Ashtekar) Integral calculus on the space of gauge…

General Relativity and Quantum Cosmology · Physics 2011-04-15 Jerzy Lewandowski

Runge's method is a tool to figure out integral points on curves effectively in terms of height. This method has been generalised to varieties of any dimension, unfortunately its conditions of application are often too restrictive. In this…

Number Theory · Mathematics 2019-03-06 Samuel Le Fourn

The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…

Numerical Analysis · Computer Science 2019-03-21 Hai D. Huynh , Phuong Tran , Xiaoying Zhuang , H. Nguyen-Xuan

We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral equation techniques that allow for the efficient and accurate evaluation of quantities needed in…

Numerical Analysis · Mathematics 2020-01-28 Akash Anand , Jeffrey S. Ovall , Samuel Reynolds , Steffen Weißer

We develop a finite element method for the Laplace--Beltrami operator on a surface described by a set of patchwise parametrizations. The patches provide a partition of the surface and each patch is the image by a diffeomorphism of a…

Numerical Analysis · Mathematics 2017-08-02 Tobias Jonsson , Mats G. Larson , Karl Larsson

We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then…

Numerical Analysis · Mathematics 2025-10-20 Douglas N. Arnold , Daniele Boffi , Richard S. Falk

By adopting the standard definition of diffeomorphisms for a Regge surface we give an exact expression of the Liouville action both for the sphere and the torus topology in the discretized case. The results are obtained in a general way by…

High Energy Physics - Theory · Physics 2009-10-30 Pietro Menotti , Pier Paolo Peirano

Using integrability, we construct (to leading order in perturbation theory) the explicit form of twist-three light-ray operators in planar $\mathcal{N}=4$ SYM. This construction allows us to directly compute analytically continued CFT data…

High Energy Physics - Theory · Physics 2024-09-05 Alexandre Homrich , David Simmons-Duffin , Pedro Vieira

This paper proposes and analyzes a class of new weak Galerkin (WG) finite element methods for 2- and 3-dimensional linear elasticity problems. The methods use discontinuous piecewise-polynomial approximations of degrees $k(\geq 0)$ for the…

Numerical Analysis · Mathematics 2017-10-24 Gang Chen , Xiaoping Xie