Time‐accurate solution of stabilized convection–diffusion–reaction equations: II—accuracy analysis and examples | Zendy

Huerta Antonio | Zendy; Roig Bernardino | Zendy; Donea Jean | Zendy

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Time‐accurate solution of stabilized convection–diffusion–reaction equations: II—accuracy analysis and examples

Author(s) -

Huerta Antonio,

Roig Bernardino,

Donea Jean

Publication year - 2002

Publication title -

communications in numerical methods in engineering

Language(s) - English

Resource type - Journals

eISSN - 1099-0887

pISSN - 1069-8299

DOI - 10.1002/cnm.518

Subject(s) - galerkin method , petrov–galerkin method , convection–diffusion equation , finite element method , mathematics , upwind scheme , diffusion , grid , transient (computer programming) , work (physics) , scale (ratio) , computer science , convection , mathematical analysis , mechanics , geometry , physics , discretization , thermodynamics , operating system , quantum mechanics

The paper addresses the development of time‐accurate methods for solving transient convection–diffusion –reaction problems using finite elements. The accuracy characteristics of the spatially stabilized implicit multi‐stage time‐stepping schemes developed in a companion paper (Part I of this work) are analysed and compared here. This is done by means of a Fourier analysis. An important improvement is observed when the order of the method is increased. Moreover, the stabilization techniques proposed (streamline‐upwind Petrov–Galerkin (SUPG), Galerkin least‐square (GLS), sub‐grid scale (SGS) and least squares) do not degrade the phase accuracy. Finally, some examples are presented to show the applicability of these schemes. Copyright © 2002 John Wiley & Sons, Ltd.

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