The solution of time-dependent pdes with discrete-time static remeshing is considered with a method-of-lines framework. Numerical examples in 2D (Navier Stokes) and 1D (model problems) are used to show that spatial interpolation error may have an important impact on the efficiency of integration. Analysis is used to confirm these results and a test for monitoring this potential source of problems suggested. An improved positivity preserving quadratic interpolant is introduced as an aid to improving matters on triangular and tetrahedral meshes. Finally a new solution-based mesh quality indicator is used to measure the quality of triangular and tetrahedral meshes with respect to the solution.}

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1996-1997 Mathematics in High Performance Computing