Adaptive finite element approximation of coupled flow and transport problems with applications in heat transfer

International Journal for Numerical Methods in Fluids

Volumn 57, Issue 9, 2008, Pages 1397-1420

  Larson, Mats G ^a   Söderlund, Robert ^a   Bengzon, Fredrik ^a  

^a UMEÅ UNIVERSITY   (Sweden)

Author keywords

Adaptivity; Advection diffusion equation; Error estimation; Finite element methods; Mesh adaptation; Navier Stokes

Indexed keywords

APPROXIMATION THEORY; COUPLED CIRCUITS; ESTIMATION; FINITE ELEMENT METHOD; FLOW OF FLUIDS; HEAT EXCHANGERS; HEAT TRANSFER; HEATING EQUIPMENT; POLYNOMIAL APPROXIMATION; THERMOANALYSIS; THREE DIMENSIONAL;

A POSTERIORI; ADAPTIVE FINITE ELEMENT METHODS; ADAPTIVE FINITE ELEMENTS; ADAPTIVE METHODS; ADAPTIVITY; ADVECTION-DIFFUSION EQUATION; COOLING FLUIDS; COUPLED FLOW; COUPLED PROBLEMS; DUALITY TECHNIQUES; ERROR ESTIMATION; FINITE ELEMENT METHODS; FLOW AND HEAT TRANSFER; INCOMPRESSIBLE FLUID FLOW; INTEGRATED HEAT; MESH ADAPTATION; NAVIER-STOKES; TEST CASES; TIME-DEPENDENT FLOWS; VARIATIONAL APPROXIMATION;

ERROR ANALYSIS;

EID: 48549105913     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1818     Document Type: Conference Paper

References (24)

1. Larson MG, Bengzon F. Adaptive finite element approximation of multiphysics problems. Communications in Numerical Methods in Engineering 2007; DOI: 10.1002/cnm.1087.
2. Larson MG, Målqvist A. Goal oriented adaptivity for coupled flow and transport problems with applications in oil reservoir simulations. Computer Methods in Applied Mechanics and Engineering 2007; 196(37-40):3546-3561.
3. Carey V, Estep D, Tavener S. A posteriori analysis and adaptive error control for operator decomposition methods for coupled elliptic systems. I: one way coupled systems. SIAM Journal on Numerical Analysis 2006; in revision.
4. Carey V, Estep D, Tavener S. A posteriori analysis and adaptive error control for operator decomposition methods for elliptic systems II: fully coupled systems. 2007; in preparation.
5. Guermond JL, Minev P, Shen J. An overview of projection methods for incompressible flows. Computer Methods in Applied Mechanics and Engineering 2006; 195(44-47):6011-6045.
6. Becker R, Heuveline V, Rannacher R. An optimal control approach to adaptivity in computational fluid mechanics. International Journal for Numerical Methods in Fluids 2002; 40(1-2):105-120 (ICFD Conference on Numerical Methods for Fluid Dynamics, Oxford, 2001).
7. Hoffman J, Johnson C. Computational Turbulent Incompressible Flow. Applied Mathematics: Body and Soul, vol. 4. Springer: Berlin, 2007.
8. Bangerth W, Rannacher R. Adaptive Finite Element Methods for Differential Equations. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag: Basel, 2003.
9. Eriksson K, Estep D, Hansbo P, Johnson C. Introduction to adaptive methods for differential equations. Acta Numerica 1995; 4:105-158.
10. Estep DJ, Larson MG, Williams RD. Estimating the error of numerical solutions of systems of reaction-diffusion equations. Memoirs of the American Mathematical Society 2000; 146(696):viii + 109.
11. Carey GF. Computational Grids: Generation, Adaptation, and Solution Strategies. Series in Computational and Physical Processes in Mechanics and Thermal Sciences. Taylor & Francis: Washington, DC, 1997.
12. Giles MB, Larson MG, Levenstam J, Suli E. Adaptive error control for finite element approximations of the lift and drag in viscous flow. Technical Report, NA97/06, Oxford University Computing Laboratory, 1997.
13. Carey GF, Chow S-S, Seager MK. Approximate boundary-flux calculations. Computer Methods in Applied Mechanics and Engineering 1985; 50(2):107-120.
14. Hughes TJR, Engel G, Mazzei L, Larson MG. The continuous Galerkin method is locally conservative. Journal of Computational Physics 2000; 163(2):467-488.
15. Wildey T, Tavener S, Estep D. A posteriori error estimation of approximate boundary fluxes. Communications in Numerical Methods in Engineering 2006; DOI: 10.1002/cnm.1014.
16. Tritton DJ. Physical Fluid Dynamics (2nd edn). Oxford Science Publications, The Clarendon Press/Oxford University Press: New York, 1988.
17. Rannacher R. Finite element methods for the incompressible Navier-Stokes equations. Fundamental Directions in Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser: Basel, 2000; 191-293.
18. Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability. The International Series of Monographs on Physics. Clarendon Press: Oxford, 1961.
19. Larson MG, Söderlund R. Adaptive finite element approximation of two way coupled problems. Research Report in Mathematics No. 10, Umeå University, 2007. ISBN: 978-91-7264-482-3, ISSN: 1653-0810.
20. Brenner SC, Scott LR. The Mathematical Theory of Finite Element Methods (2nd edn). Texts in Applied Mathematics, vol. 15. Springer: New York, 2002.
21. Scott LR, Zhang S. Finite element interpolation of nonsmooth functions satisfying boundary conditions. Mathematics of Computation 1990; 54(190):483-493.
22. Tezduyar TE. Stabilized Finite Element Formulations for Incompressible Flow Computations. Advances in Applied Mechanics, vol. 28. Academic Press: Boston, MA, 1992; 1-44.
23. Thomée V. Galerkin Finite Element Methods for Parabolic Problems (2nd edn). Springer Series in Computational Mathematics, vol. 25. Springer: Berlin, 2006.
24. Johnson C. Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press: Cambridge, 1987.