A New Class of Stabilized WEB-Spline-Based Mesh-Free Finite Elements for the Approximation of Maxwell Equations

Abstract

The objective of this article is to discuss the existence and the uniqueness of a weighted extended B-spline-(WEB-spline) based discrete solution for the Maxwell equations in low frequency limit. The domain is composed of insulating and conducting regions. This problem has saddle point structure where the electric field in insulating region is the Lagrange multiplier that forces curl-free constraint on the magnetic field.

WEB-Spline-based mesh-free finite element approximation forp-Laplacian

“…Another important issue to be addressed while choosing finite elements for the approximation of the Stokes and Navier-Stokes equations is the fulfilment of the so-called inf-sup condition [7]. A class of WEB-Spline-based stable elements that satisfy such an inf-sup condition has been developed by Chaudhary and Srinivas Kumar [8] and Srinivas et al [24,25]. The objective of this paper is to develop web spline-based mesh-free finite element approximation procedure for solving p-Laplace equation.…”

WEB‐spline based mesh‐free finite element analysis for the heat equation and the time‐dependent Navier–Stokes equation: A survey

“…A class of web-spline based stable elements that satisfy such an inf-sup condition has been developed by the authors Srinivas et al in Refs. [10][11][12][13][14]. The aim of this study is to use web-spline for solving parabolic equations [15], especially diffusion equations, time-dependent Stokes, and Navier-Stokes equations.…”