Abstract

Verification of codes that numerically approximate solutions of partial differential equations consists in demonstrating that the codeCode is free of coding errors and is capable, given sufficient discretization, of approaching exact mathematical solutions. This requires the evaluation of discretization errorsDiscretization error using known benchmarkBenchmark solutions. The best benchmarks are exact analytical solutionsAnalytical solution with a sufficiently complex solution structure; they need not be physically realistic since verification is a purely mathematical exercise. The Method of Manufactured Solutions provides a straightforward and general procedure for generating such solutions. For complex codesCode, the method utilizes symbolic manipulation, but here it is illustrated with simple examples. When used with systematic gridGrid refinement studies, which are remarkably sensitive, MMS can produce robust code verificationsCode verification with a strong completion point.