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Reference Solutions

Reference solutions are provided for some problems for which the exact solution is not known. For many uses, such as computing a norm of the error of an approximate solution or examining the convergence rate of a sequence of approximate solutions, the reference solution can be used in lieu of the exact solution, provided the approximate solution is not more accurate than the reference solution.

The NIST AMR Benchmark Reference Solutions are C0 piecewise polynomial functions over a mesh of simplicies (intervals, triangles, tetrahedra). The degree of the polynomials is constant over the mesh, but the simplex size may vary.

The reference solutions are provided in a text file. Those compressed with bzip2 or gzip follow the Unix end of line convension, and those compressed with zip follow the dos convension. The format of a NIST AMR Benchmark Reference Solution file is available as a PDF file.

Fortran software to evaluate a reference solution at a given set of points and to obtain other information about the reference solution (for example, error estimates and the mesh size) is available with Unix convensions in AMRrefsoln-1.2.0.tar.gz and with dos convensions in The README file is available for previewing the capabilities of the software.

The National Institute of Standards and Technology (NIST) is an agency of the U.S. Department of Commerce.

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Date created: August 20, 2015 | Last updated: March 6, 2018    Contact: William Mitchell, Home Page
Development status: Not Maintained