Weighted Extended B-Spline Finite Element Analysis of a coupled system of general Elliptic equations
For researchers in numerical PDEs, this provides a meshless FE approach for complex coupled elliptic systems, but the contribution is incremental as it extends existing WEBS methods to a new problem class.
This paper proves existence and uniqueness of solutions for a coupled system of general elliptic equations and develops a meshless finite element method using weighted extended B-spline functions, with convergence established via a priori error estimates and validated on numerical examples.
In this study we establish the existence and uniqueness of the solution of a coupled system of general elliptic equations with anisotropic diffusion , non-uniform advection and variably influencing reaction terms on Lipschitz continuous domain $Ω\subset \mathbb{R}^m $ (m$\geq$1) with a Dirichlet boundary. Later we consider the finite element (FE) approximation of the coupled equations in a meshless framework based on weighted extended B-Spine functions (WEBS).The a priori error estimates corresponding to the finite element analysis are derived to establish the convergence of the corresponding FE scheme and the numerical methodology has been tested on few examples.