# A Posteriori Error Estimates with Boundary Correction for a Cut Finite Element Method

## TL;DR

This paper develops residual-based a posteriori error estimates for the CutFEM method applied to elliptic problems with complex boundaries, ensuring robustness and accounting for boundary geometry and data approximation.

## Contribution

It introduces a new a posteriori error estimation framework for CutFEM that is reliable, efficient, and robust to boundary cuts, including boundary geometry and data approximation.

## Key findings

- Reliability and efficiency of the error estimator are theoretically proven.
- Constants in the estimates are robust with respect to boundary cuts.
- The method effectively handles non-polygonal boundaries in elliptic problems.

## Abstract

In this work we study a residual based a posteriori error estimation for the CutFEM method applied to an elliptic model problem. We consider the problem with non-polygonal boundary and the analysis takes into account the geometry and data approximation on the boundary. The reliability and efficiency are theoretically proved. Moreover, constants are robust with respect to how the domain boundary cuts the mesh.