# Recovery of the Interface Velocity for the Incompressible Flow in Enhanced Velocity Mixed Finite Element Method

## TL;DR

This paper improves the accuracy of interface velocity approximation in incompressible flow simulations using an enhanced velocity mixed finite element method and a post-processed pressure reconstruction, leading to better convergence.

## Contribution

It introduces a novel velocity reconstruction method at interfaces using post-processed pressure to enhance approximation accuracy in mixed finite element methods.

## Key findings

- Improved convergence rate at interfaces.
- Enhanced velocity approximation accuracy.
- Numerical validation confirms effectiveness.

## Abstract

The velocity, coupling term in the flow and transport problems, is important in the accurate numerical simulation or in the posteriori error analysis for adaptive mesh refinement. We consider Enhanced Velocity Mixed Finite Element Method for the incompressible Darcy flow. In this paper, our aim to study the improvement of velocity at interface to achieve the better approximation of velocity between subdomains. We propose the reconstruction of velocity at interface by using the post-processed pressure. Numerical results at the interface show improvement on convergence rate.