# A convergent boundary-condition conforming adaptive spline-based finite element method for the bi-Laplace operator

## TL;DR

This paper proves the convergence of an adaptive spline-based finite element method designed for solving the bi-Laplace operator, a fourth-order elliptic problem, enhancing numerical solution reliability.

## Contribution

It introduces a convergent adaptive spline-based finite element method specifically for the bi-Laplace operator, advancing numerical techniques for high-order elliptic problems.

## Key findings

- Proves convergence of the proposed method
- Enhances numerical solution accuracy for the bi-Laplace operator
- Provides theoretical foundation for adaptive spline methods

## Abstract

We establish the convergence of an adaptive spline-based finite element method of a fourth order elliptic problem.