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**Approximate boundary-flux calculations.**
*(English)*
Zbl 0546.73057

A technique for determining derivatives (fluxes or stresses) from finite element solutions is developed. The approach is a generalization to higher dimensions of a procedure known to give highly accurate results in one dimension. Numerical experiments demonstrate that certain difficulties are associated with corners in the higher-dimensional extensions and two variants of the method are examined. We consider both triangular and quadrilateral elements and observe some interesting differences in the numerical rates of convergence. Finally, this post- processing scheme is tested for nonlinear problems.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74S99 | Numerical and other methods in solid mechanics |

### Keywords:

derivatives; fluxes; stresses; generalization to higher dimensions; Numerical experiments; triangular and quadrilateral elements; rates of convergence; post-processing scheme; nonlinear problems
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\textit{G. F. Carey} et al., Comput. Methods Appl. Mech. Eng. 50, 107--120 (1985; Zbl 0546.73057)

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### References:

[1] | Carey, G. F.: Derivative calculations from finite element solutions. Comput. meths. Appl. mech. Engrg. 35, 1-14 (1982) · Zbl 0478.73052 |

[2] | Carey, G. F.; Wheeler, M. F.: C0-collocation-Galerkin methods. Lecture notes in computer science, 250-256 (1979) |

[3] | Douglas, J.; Dupont, T.; Wheeler, M. F.: A Galerkin procedure for approximating the flux on the boundary for elliptic and parabolic boundary-value problems. R.a.i.r.o. 2, 47-59 (1974) · Zbl 0315.65063 |

[4] | Dupont, T.: A unified theory of superconvergence for Galerkin methods for two-point boundary problems. SIAM J. Numer. anal. 13, No. 3, 362-368 (1976) · Zbl 0332.65050 |

[5] | Wheeler, M. F.: A Galerkin procedure for estimating the flux for two-point boundary-value problems using continuous piecewise-polynomial spaces. Numer. math. 22, 99-109 (1974) |

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