# Virtual Enriching Operators

## TL;DR

This paper introduces bounded linear operators that transform $H^1$ finite element spaces into $H^2$ virtual element spaces, aiding the analysis of advanced finite element methods in 2D and 3D.

## Contribution

It constructs new operators bridging $H^1$ and $H^2$ spaces, enhancing the theoretical framework for nonstandard finite element analysis.

## Key findings

- Operators are bounded and linear.
- Applicable in 2D and 3D finite element contexts.
- Facilitates analysis of nonstandard methods.

## Abstract

We construct bounded linear operators that map $H^1$ conforming Lagrange finite element spaces to $H^2$ conforming virtual element spaces in two and three dimensions. These operators are useful for the analysis of nonstandard finite element methods.