Non uniform weighted extended B-Spline finite element analysis of non linear elliptic partial differential equations

TL;DR

This paper introduces a non-uniform web spline finite element method for solving nonlinear elliptic PDEs, providing theoretical analysis including well-posedness and error estimates with convergence rates.

Contribution

It presents a novel non-uniform web spline finite element approach for nonlinear elliptic PDEs, with rigorous analysis of stability and convergence.

Findings

Proves well-posedness of the proposed method

Derives a priori error estimates with convergence rate $oldsymbol{ extit{O}(h^{oldsymbol{ extit{ extalpha}}})}$

Demonstrates effectiveness for gradient-type nonlinear elliptic equations

Abstract

We propose a non uniform web spline based finite element analysis for elliptic partial differential equation with the gradient type nonlinearity in their principal coefficients like p-laplacian equation and Quasi-Newtonian fluid flow equations. We discuss the well-posednes of the problems and also derive the apriori error estimates for the proposed finite element analysis and obtain convergence rate of $\mathcal{O}(h^{\alpha})$ for $\alpha > 0$.