# Some error estimates for the DEC method in the plane

## TL;DR

This paper demonstrates that the Discrete Exterior Calculus (DEC) method for the Poisson problem in the plane can be viewed as a box method, providing error estimates and comparing its performance to finite element methods.

## Contribution

It establishes a connection between DEC and the box method, deriving error estimates and highlighting additional virtues of DEC beyond convergence.

## Key findings

- DEC is comparable to linear finite element methods in accuracy.
- Error estimates for DEC are established.
- DEC has virtues beyond convergence, such as geometric flexibility.

## Abstract

We show that the Discrete Exterior Calculus (DEC) method can be cast as the earlier box method for the Poisson problem in the plane. Consequently, error estimates are established, proving that the DEC method is comparable to the Finite Element Method with linear elements. We also discuss some virtues, others than convergence, of the DEC method.