Related papers: Foundations of space-time finite element methods: …
It is shown that for every problem within dimensional regularization, using the Integration-By-Parts method, one is able to construct a set of master integrals such that each corresponding coefficient function is finite in the limit of…
We generalize the two dimensional mixed finite elements of Arbogast and Correa [T. Arbogast and M. R. Correa, SIAM J. Numer. Anal., 54 (2016), pp. 3332--3356] defined on quadrilaterals to three dimensional cuboidal hexahedra. The…
Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these…
This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…
In this work we present a generic framework for non-conforming finite elements on polytopal meshes, characterised by elements that can be generic polygons/polyhedra. We first present the functional framework on the example of a linear…
The purpose of this paper is to discuss representations of high order $C^0$ finite element spaces on simplicial meshes in any dimension. When computing with high order piecewise polynomials the conditioning of the basis is likely to be…
This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange…
Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our…
This paper applies a complete parametric set for approximating the geometry of a quadrilateral element. The approximation basis used is a complete Pascal polynomial of second order with six free parameters. The interpolation procedure is a…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
We give a systematic and self-contained account of the construction of geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we elaborate upon a previously overlooked basis for one of the…
The use of orthonormal polynomial bases has been found to be efficient in preventing ill-conditioning of the system matrix in the primal formulation of Virtual Element Methods (VEM) for high values of polynomial degree and in presence of…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific challenges due to their inherently non-conforming nature and, in…
This paper studies the thermo-poroelasticity model. By introducing an intermediate variable, we transform the original three-field model into a four-field model. Building upon this four-field model, we present both a coupled finite element…
We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on…
This paper introduces a novel tangential-normal ($t$-$n$) decomposition for finite element differential forms, presenting a new framework for constructing bases in finite element exterior calculus. The main contribution is the development…
A new numerical method is presented for solving the rotating shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical…
The Frenet apparatus is a new framework for constructing high order geometry-conforming immersed finite element functions for interface problems. In this report, we present a procedure for constructing the local IFE bases in some detail as…
We consider the lowest--degree nonconforming finite element methods for the approximation of elliptic problems in high dimensions. The $P_1$--nonconforming polyhedral finite element is introduced for any high dimension. Our finite element…