Review of code and solution verification procedures for computational simulation.

*(English)*Zbl 1072.65118Summary: Computational simulation can be defined as any computer application which involves the numerical solution to a system of partial differential equations. A broad overview is given of verification procedures for computational simulation. The two aspects of verification examined are code verification and solution verification. Code verification is a set of procedures developed to find coding mistakes that affect the numerical discretization. The method of manufactured solutions combined with order of accuracy verification is recommended for code verification, and this procedure is described in detail. Solution verification is used to estimate the numerical errors that occur in every computational simulation.

Both round-off and iterative convergence errors are discussed, and a posteriori methods for estimating the discretization error are examined. Emphasis is placed on discretization error estimation methods based on Richardson extrapolation as they are equally applicable to any numerical method. Additional topics covered include calculating the observed order of accuracy, error bands, and practical aspects of mesh refinement.

Both round-off and iterative convergence errors are discussed, and a posteriori methods for estimating the discretization error are examined. Emphasis is placed on discretization error estimation methods based on Richardson extrapolation as they are equally applicable to any numerical method. Additional topics covered include calculating the observed order of accuracy, error bands, and practical aspects of mesh refinement.

##### MSC:

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

65G20 | Algorithms with automatic result verification |

65Y20 | Complexity and performance of numerical algorithms |

35Q53 | KdV equations (Korteweg-de Vries equations) |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |

65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |

##### Keywords:

numerical examples; Burgers equation; system of partial differential equations; computational simulation; code verification; solution verification; convergence; error estimation; Richardson extrapolation; mesh refinement##### Software:

CGM
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\textit{C. J. Roy}, J. Comput. Phys. 205, No. 1, 131--156 (2005; Zbl 1072.65118)

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