2. Benchmark solution#

2.1. Calculation method used for reference solutions#

In such a case, it is not possible to unearth an analytical solution! The reference solution used for calculating errors on the mean temperature of GM35 (modeling A) and on the potential energy of deformation (modeling A and B), is in fact an approximate solution obtained after a series of three uniform refinements. This uniform refinement procedure can be driven by a PYTHON loop and the MACR_ADAP_MAIL option UNIFORME operator.

2.2. Benchmark result#

Modeling A:

Potential deformation energy (purely thermal) = \(–2016.80291J\)

Average temperature on GM35 = \(170.2°Cm\)

Modeling B:

Potential deformation energy (thermo-mechanical) = \(\mathrm{6.75073756.}{10}^{–}5J\)

2.3. Uncertainty about solutions#

They are only approximate solutions obtained on a « virtually converged » mesh.

2.4. Bibliographical references#

    1. DESROCHES. « Zhu-Zienkiewicz error estimators in 2D elasticity ». [R4.10.01], 1994.

    1. DESROCHES. « Residual error estimator ». [R4.10.02], 2000.

    1. BOITEAU. « Residual spatial error indicators for transient thermals ». [R4.10.03], 2001.

  4. O. BOITEAU. « Courses and TP Error Indicators & Mesh Adaptation; State of the art and implementation in the Code_Aster ». `http://www.code‑aster.com/utilisation/formations`_ < http://www.code-aster.com/utilisation/formations>, 2002.

    1. BOITEAU. « FORMA04: Mechanical adaptive mesh on a flexure beam ». [V6.03.119], 2002.