WEB-spline based mesh-free finite element analysis for the heat equation and the time-dependent Navier-Stokes equation: A survey (Q2846184)

This article deals with the use of WEB-spline based mesh-free finite element method for the heat equation and the time-dependent Navier-Stokes equations. The authors discuss the WEB-spline approach for the Poisson problem in the first section and state the properties of the discretization. The WEB-spline method for the diffusion equation with homogeneous Dirichlet boundary conditions is considered next and results concerning the existence of a solution are provided. The authors prove a stability result in terms of the energy norm in the subsequent section. The main part of the paper deals with the WEB-spline method for unsteady Stokes and Navier-Stokes equations. Linear-constant and quadratic-linear elements are considered in the discretization, and existence and uniqueness results as well as error estimates for each type of problem are stated. The final section of the article contains numerical examples that illustrate use of the WEB-spline method for steady state diffusion and the stationary Stokes equations in two dimensions.