Error estimates and mesh adaption for a cell vertex finite volume scheme
In this paper we investigate a posteriori error estimates for the cell vertex finite volume method and their applicability to adaptive mesh generation. We start from the cell vertex scheme reformulated as a Petrov-Galerkin finite element method and base the error estimate on the calculation of the finite element residual of the approximate solution. An analogy can be made between the residual in finite element methods and the truncation error of finite difference schemes. Numerical investigation of the performance of the error indicator for a model problem of two dimensional advection demonstrate its reliability and efficiency. The error indicator is then applied to a transonic Euler calculation where it is contrasted with an alternative procedure based on first and second differences of physical flow quantities which can be related to local interpolation error. Finally, we discuss the effective use of error estimates in adaptive mesh generation.
KeywordsTruncation Error Posteriori Error Estimate Error Indicator Local Truncation Error Posteriori Error Estimator
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- H. Cartan. Calcul Différentiel. Herrmann, 1967.Google Scholar
- P.I. Crumpton, J.A. Mackenzie, and K.W. Morton. Cell vertex algorithms for the compressible Navier-Stokes equations. Technical Report NA91/12, Oxford University Computing Laboratory, 11 Keble Road, Oxford, OX1 3QD, 1991. Submitted for publication.Google Scholar
- R.G. Jones. Error estimators for adaptive methods. Technical Report NA90/17, Oxford University Computing Laboratory, 11 Keble Road, Oxford, OX1 3QD, 1990.Google Scholar
- A.J. Mayfield. Discussion and presentation of a new method for mesh movement. Technical Report NA92/11, Oxford University Computing Laboratory, 11 Keble Road, Oxford, OX1 3QD, 1992.Google Scholar
- A.J. Mayfield. Design and implementation of an adaptive multigrid algorithm. D.Phil thesis, Oxford University, 1992.Google Scholar
- A.J. Mayfield. A new efficient data structure for mesh enrichment algorithms. Technical Report NA92/12, Oxford University Computing Laboratory, 11 Keble Road, Oxford, OX1 3QD, 1992.Google Scholar
- H. Schlichting. Boundary-Layer Theory. McGraw-Hill, 1955.Google Scholar
- E. Sùli. Finite volume methods on distorted meshes: stability, accuracy, adaptivity. Technical Report NA89/6, Oxford University Computing Laboratory, 11 Keble Road, Oxford, OX1 3QD, 1989.Google Scholar