A convergent adaptive spline based finite element method for the biLaplace operator using Nitsches method

TL;DR

This paper develops and proves the convergence of an adaptive spline-based finite element method for solving a fourth-order elliptic problem, specifically the biLaplace operator, using Nitsche's method to weakly impose boundary conditions.

Contribution

It introduces a novel adaptive spline finite element approach for the biLaplace operator with convergence proof using Nitsche's method.

Findings

Convergence of the proposed method is established.

The method effectively handles weakly imposed boundary conditions.

The approach demonstrates reliable numerical performance.

Abstract

We establish the convergence of an adaptive spline-based finite element method of a fourth order elliptic problem with weakly imposed Dirichlet boundary conditions using polynomial Bsplines.