Weighted Extended B-Spline Finite Element Analysis of a coupled system of general Elliptic equations

TL;DR

This paper develops a finite element method using weighted extended B-spline functions to solve coupled elliptic equations with complex features, proving convergence and demonstrating effectiveness through numerical tests.

Contribution

It introduces a meshless finite element approach with weighted extended B-spline functions for coupled elliptic systems, including error analysis and numerical validation.

Findings

Established existence and uniqueness of solutions.

Derived a priori error estimates for the FE scheme.

Validated the numerical method with example tests.

Abstract

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 $\Omega \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.