Benchmark solution
====


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.


Benchmark result
----

**Modeling A:**

Potential deformation energy (purely thermal) = :math:`–2016.80291J`

Average temperature on GM35 = :math:`170.2°Cm`

**Modeling B:**

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


Uncertainty about solutions
----

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


Bibliographical references
----


1.  X. DESROCHES. "Zhu-Zienkiewicz error estimators in 2D elasticity". [:ref:`R4.10.01 <R4.10.01>`], 1994.


2.  X. DESROCHES. "Residual error estimator". [:ref:`R4.10.02 <R4.10.02>`], 2000.


3.  O. BOITEAU. "Residual spatial error indicators for transient thermals". [:ref:`R4.10.03 <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.


5.  O. BOITEAU. "FORMA04: Mechanical adaptive mesh on a flexure beam". [:ref:`V6.03.119 <V6.03.119>`], 2002.