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Stabilized Moving Finite Elements for Convection Dominated Problems

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Abstract

The Moving Finite Element method (MFE) when applied to purely hyperbolic problems tends to move its nodes with the flow (often a good thing). But for steady or near steady problems the nodes flow past stationary regions of critical interest and pile up at the outflow. We report on efforts to develop moveable node versions of the “stabilized” finite element methods which have so successfully improved upon Galerkin in the fixed node setting. One method in particular (Galerkin-Δx TLSMFE with a “fix”) yields very promising results on our simple 1-D model problem. Its nodes lock onto and resolve sharp stationary features but also lock onto and move with the moving features of the solution.

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References

  1. Baines (1994) Moving Finite Elements Oxford University Press Oxford

    Google Scholar 

  2. A. Brooks T.J.R. Hughes (1982) ArticleTitleStreamline upwind/Petrov–Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations Comput. Methods Appl. Mech. Eng. 32 199–259 Occurrence Handle10.1016/0045-7825(82)90071-8

    Article  Google Scholar 

  3. N.N. Carlson K. Miller (1998) ArticleTitleDesign and application of a gradient-weighted moving finite element code I: in one dimension SIAM J. Sci. Comput. 19 728–765 Occurrence Handle10.1137/S106482759426955X

    Article  Google Scholar 

  4. N.N. Carlson K. Miller (1998) ArticleTitleDesign and application of a gradient-weighted moving finite element code II: in two dimensions SIAM J. Sci. Comput. 19 766–798 Occurrence Handle10.1137/S1064827594269561

    Article  Google Scholar 

  5. L.P. Franca T.J.R. Hughes (1993) ArticleTitleConvergence analysis of Galerkin/ least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier–Stokes equations Comput. Methods Appl. Mech. Eng. 105 285–298 Occurrence Handle10.1016/0045-7825(93)90126-I

    Article  Google Scholar 

  6. T.J.R. Hughes (1995) ArticleTitleMultiscale phonomena: Green’s functions, the Dirichlet-to-Neumann. formulation, subgrid scale models, bubbles and the origins of stabilized methods Comput. Methods Appl. Mech. Eng. 127 387–401 Occurrence Handle10.1016/0045-7825(95)00844-9

    Article  Google Scholar 

  7. K. Miller (1981) ArticleTitleMoving finite elements II SIAM J. Numer. Anal. 18 1033–1057 Occurrence Handle10.1137/0718071

    Article  Google Scholar 

  8. K. Miller (1997) ArticleTitleA geometrical-mechanical interpretation of gradient-weighted moving finite elements SIAM J. Numer. Anal. 34 67–90 Occurrence Handle10.1137/S0036142994260884

    Article  Google Scholar 

  9. Miller K. (2005). Nonlinear Krylov and moving nodes in the Method of Lines. To appear in J. Comp. Appl. Math.

  10. K. Miller M.J. Baines (1998) Least squares moving finite elements Oxford University Computing Laboratory Oxford

    Google Scholar 

  11. K. Miller M.J. Baines (2001) ArticleTitleLeast squares moving finite elements IMA J. Numer. Anal. 21 621–642 Occurrence Handle10.1093/imanum/21.3.621

    Article  Google Scholar 

  12. K. Miller R.N. Miller (1981) ArticleTitleMoving finite elements I SIAM J. Numer. Anal. 18 1019–1032 Occurrence Handle10.1137/0718070

    Article  Google Scholar 

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Correspondence to Keith Miller.

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Miller, K. Stabilized Moving Finite Elements for Convection Dominated Problems. J Sci Comput 24, 163–182 (2005). https://doi.org/10.1007/s10915-004-4612-z

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  • DOI: https://doi.org/10.1007/s10915-004-4612-z

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