Numerical Solutions of the 1D Convection–Diffusion–Reaction and the Burgers Equation Using Implicit Multi-stage and Finite Element Methods

C. A. Ladeia () and N. M. L. Romeiro ()
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C. A. Ladeia: State University of Londrina
N. M. L. Romeiro: State University of Londrina

Chapter Chapter 15 in Integral Methods in Science and Engineering, 2013, pp 205-216 from Springer

Abstract: Abstract In this work we apply the semi-discrete formulation, where the time variable is discretized using an implicit multi-stage method and the space variable is discretized using the finite element method, to obtain numerical solutions for the 1D convection–diffusion–reaction and the Burgers equation, whose analytical solutions are known. More specifically, we use the implicit multi-stage method of second and fourth-order for time discretization. For space discretization, we use three finite elements methods, least square (LSFEM), Galerkin (GFEM) and streamline-upwind Petrov-Galerkin (SUPG). We present an error analysis, comparing the numerical with analytical solutions. We verify that the implicit multi-stage second-order method when combined with the LSFEM, GFEM and SUPG, increased the region of convergence of the numerical solutions. LSFEM presented the better performance when compared to GFEM and SUPG.

Keywords: 1D convection–diffusion–reaction equation; Burgers equation; Implicit multi-stage methods; Finite elements methods (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7828-7_15

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DOI: 10.1007/978-1-4614-7828-7_15

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