DeepAI
Log In Sign Up

UFL Dual Spaces, a proposal

01/13/2021
by   David A. Ham, et al.
0

This white paper highlights current limitations in the algebraic closure Unified Form Language (UFL). UFL currently represents forms over finite element spaces, however finite element problems naturally result in objects in the dual to a finite element space, and operators mapping between primal and dual finite element spaces. This document sketches the relevant mathematical areas and proposes changes to the UFL language to support dual spaces as first class types in UFL.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/26/2021

Conforming finite element DIVDIV complexes and the application for the linearized Einstein-Bianchi system

This paper presents the first family of conforming finite element divdiv...
04/20/2016

An algorithm for the optimization of finite element integration loops

We present an algorithm for the optimization of a class of finite elemen...
07/25/2022

A primal finite element scheme of the 𝐇(𝐝)∩𝐇() elliptic problem

In this paper, a unified family, for n⩾2 and 1⩽ k ⩽ n-1, of finite eleme...
05/06/2020

Orthogonality relations of Crouzeix-Raviart and Raviart-Thomas finite element spaces

Identities that relate projections of Raviart-Thomas finite element vect...
09/02/2019

Gibbs Phenomena for L^q-Best Approximation in Finite Element Spaces -- Some Examples

Recent developments in the context of minimum residual finite element me...
12/23/2019

Symmetry and Invariant Bases in Finite Element Exterior Calculus

We study symmetries of bases and spanning sets in finite element exterio...
07/07/2021

Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

In finite element calculations, the integral forms are usually evaluated...