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.

翻译：白皮书强调了代数封闭统一格式语言(UFL)目前存在的局限性。 UFL目前的形式超越了有限要素空间,然而,有限要素问题自然导致两个要素空间中的物体,操作员在原始元素空间和双重有限要素空间之间绘制图,本文件概述了相关数学领域,并提议修改UFL语言,以支持作为UFL头等类型的双重空间。