By Michel Krizek, Pekka Neittaanmaki, Rolf Stenberg

Those court cases originated from a convention commemorating the fiftieth anniversary of the book of Richard Courant's seminal paper, Variational equipment for difficulties of Equilibrium and Vibration. those papers tackle primary questions in numerical research and the specified difficulties that take place in making use of the finite point strategy to quite a few fields of technological know-how and engineering.

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**Example text**

The mistake can be located in any portion of the code that was exercised. It will become clearer in Chapter Six what types of coding mistakes can cause disagreement between the theoretical and observed orders-of-accuracy. If a coding mistake is suspected, it is possible to narrow down the location of the mistake by a process of elimination involving additional tests that may not have been part of the original suite of coverage tests. For example, if there was disagreement between the observed and theoretical orders-of-accuracy in a test involving a transient calculation, one could next try a steady-state test to determine if agreement could then be reached.

If the manual is inadequate, one may try consulting the code developer or, as a last resort, the source code. Code order-of-accuracy cannot be verified if one does not know precisely what equations are solved. For example, it is not enough to know that the code solves the Navier-Stokes equations. One must know the exact equations down to the last detail. If one intends to verify the full capability of the code, then one must know the full capability. For example, are the material properties permitted to be spatially variable or are they constant?

This cycle is repeated as many times as necessary until agreement between the orders-of-accuracy is obtained. If there are no further coverage tests to be run, then the results are reported and conclusions are made. If the code documentation is adequate to determine the governing equations, the theoretical order-of-accuracy, and any other critical information, there will be no need to examine the source code to perform the orderverification procedure. ” There are too many instances where having detailed knowledge of the code in question would help with the design of the coverage test suite, correct construction of the code input, and even assessment of the results.