Non uniform weighted extended B-Spline finite element analysis of non linear elliptic partial differential equations
This work provides a theoretical foundation for using non-uniform B-splines in nonlinear elliptic problems, which is an incremental contribution to numerical analysis.
The paper proposes a non-uniform weighted extended B-spline finite element method for solving nonlinear elliptic PDEs with gradient-type nonlinearity, such as the p-Laplacian and Quasi-Newtonian fluid flow equations, and proves well-posedness and convergence with rate O(h^α) for α>0.
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 $\mathcal{O}(h^α)$ for $α> 0$.