Best monitoring functions


Djokovic, D. and Damme, R.M.J. van (1998) Best monitoring functions. [Report]

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Abstract:We propose a method for a static adaptive grid method for solving partial differential equations (PDEs) using splines. The principle is based on the observation that very good grids for spline approximations can be obtained by equidistributing the error. The efficiency of the resulting adaptive method following the same principle is tested. It works quite well for all PDEs that we investigated, even when the solution develops shocks and other phenomena. The method is also applicable for PDEs whose solutions are vector-valued. In the case that the number of space dimensions is larger than one, we restrict ourselves to tensor-product splines. As to be expected, the proposed method is only efficient when the physical phenomena, {\em i.e.} shocks, are more or less aligned with (one of) the axes of the domain.
Item Type:Report
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Metis ID: 141105