%0 Journal Article
%T Applications of the Newton-Raphson method in a SDFEM for inviscid Burgers equation
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Izadi, Mohammad
%D 2020
%\ 11/01/2020
%V 8
%N 4
%P 708-732
%! Applications of the Newton-Raphson method in a SDFEM for inviscid Burgers equation
%K finite element method
%K Burgers equation
%K Newton-Raphson method
%R 10.22034/cmde.2020.32615.1513
%X In this paper we investigate in detail the applications of the classical Newton-Raphson method in connection with a space-time finite element discretization scheme for the inviscid Burgers equation in one dimensional space. The underlying discretization method is the so-called streamline diffusion method, which combines good stability properties with high accuracy. The coupled nonlinear algebraic equations thus obtained in each space-time slab are solved by the generalized Newton-Raphson method. Exploiting the band-structured properties of the Jacobian matrix, two different algorithms based on the Newton-Raphson linearization are proposed. In a series of examples, we show that in each time-step a quadratic convergence order is attained when the Newton-Raphson procedure applied to the corresponding system of nonlinear equations.
%U https://cmde.tabrizu.ac.ir/article_9920_6b55937eecf255da25814ed38b43bd59.pdf