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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 \({\varOmega }\subset {\mathbb {R}}^m \) (\(\hbox {m}\ge 1\)) 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. The a priori error estimates corresponding to the finite element analysis are derived to establish the convergence of the corresponding finite element scheme and the numerical methodology has been tested on a example.

Weighted extended B-spline finite element analysis of a coupled system of general elliptic equations