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This paper presents two types of discontinuity modeling elements (DME) that minimize the error near a discontinuity. The DME are elements that are discontinuous at one end, can satisfy continuity requirement up to seventh order at the other end, and may have polynomials of order up to fifteen. The error of approximation in the density function is measured by the L 1 norm, which is minimized with respect to the location of collocation points. Results show that the error for optimum location of collocation points in all cases is smaller than those for uniform location of collocation points and the differences in accuracy grows significantly with the order of polynomials. Two tables report the optimum location of collocation points for the DME for use by other researchers. The DME are used in conjunction with the hr-mesh refinement scheme to study modeling of stress near a stress discontinuity. Results of the study show that the recommendations for modeling density functions near a discontinuity are diametrically opposite to those recommendations for modeling of a smooth density function. |
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