Approximation of the first eigenpair of the p-Laplace operator using WEB-spline based finite element method

摘要

In this article, we consider the eigenvalue problem of the p-Laplace operator for 1 p infinity on a bounded domain with homogeneous Dirichlet boundary condition. The weighted extended b-spline (web-spline) based mesh-free finite element method is used to compute the first eigenpair. This method does not require any mesh generation and therefore, it can be implemented very efficiently. High accuracy can be achieved with relatively low dimensional approximation spaces and less computation time as compared to the usual finite element method. The numerical results are provided for different values of p on three different types of domains using web-spline of degree one.