1Blurb::
2Estimate order of convergence of a response as model fidelity increases
3Description::
4Solution verification procedures estimate the order of convergence of
5the simulation response data during the course of a refinement study.
6This branch of methods is new and currently only contains one algorithm:
7Richardson extrapolation.
8
9<b> Refinement of the model </b>
10
11The model fidelity must be parameterized by one or more continuous state variable(s).
12
13The refinement path is
14determined from the \c initial_state of the \c continuous_state
15variables specification in combination with the
16\c refinement_rate, where each of the state variables is treated as an
17independent refinement factor and each of the initial state values is
18repeatedly divided by the refinement rate value to define new
19discretization states.
20
21<b> Results </b>
22
23Three algorithm options are currently provided:
24-# \c estimate_order
25-# \c converge_order
26-# \c converge_qoi
27
28<b> Stopping Criteria </b>
29
30The method employs the
31\c max_iterations and \c convergence_tolerance method independent
32controls as stopping criteria.
33
34
35Topics::
36Examples::
37Theory::
38In each of these cases, convergence order for a response quantity of
39interest (QoI) is estimated from
40\f[p = ln\left(\frac{QoI_3 - QoI_2}{QoI_2 - QoI_1}\right)/ln(r)\f]
41where \f$r\f$ is the uniform refinement rate specified by \c
42refinement_rate.
43Faq::
44See_Also::
45