Finite Element Approximation Using WEB-Splines for the Heat Equation. (3rd October 2018)

• Record Type: Journal Article
• Authors: Patra, Suchismita; Srinivas Kumar, V. V. K.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 13(2018)
• Page Start: 1423
• Page End: 1439
• Publication Date: 2018-10-03
• Subjects: Dirichlet problem -- heat equation -- mesh-free methods -- web-spline; 41A15 -- 41A63 -- 65M12 -- 65M15 -- 65M60; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1485042
• Languages: English
• ISSNs: 0163-0563

Abstract

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.