Finite Element Approiximation Using WEB-Splines for the Heat Equation. (3rd October 2018) - Patra, Suchismita; Srinivas Kumar, V. V. K.
Abstract: In this paper we use weighted extended b -spline (web-spline) method to solve heat equation with Dirichlet boundary condition on smooth bounded domains. First we consider the semi-discrete formulation to approximate the solution in space variable by using web-splines as basis functions on regular grids. Then we consider the fully-discrete formulation of the same problem. For the time discretization we use backward Euler method. We provide a priori error estimates for both the semi-discrete and fully-discrete formulations in L 2 andH 0 1 norms and confirm them numerically by using web-splines of degree 1–3. We also have shown the comparison of results obtained via standard finite element method and web-spline method using linear basis functions.