Modified equation based mesh adaptation algorithm for evolutionary scalar partial differential equations |
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Authors: | Ritesh Kumar Dubey Prabhat Mishra |
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Affiliation: | 1. Research Institute & Department of Mathematics, SRM Institute of Science & Technology, Chennai, India;2. Department of Mathematics, SRM Institute of Science & Technology, Chennai, India |
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Abstract: | It is well known that on uniform mesh classical higher order schemes for evolutionary problems yield an oscillatory approximation of the solution containing discontinuity or boundary layers. In this article, an entirely new approach for constructing locally adaptive mesh is given to compute nonoscillatory solution by representative “second” order schemes. This is done using modified equation analysis and a notion of data dependent stability of schemes to identify the solution regions for local mesh adaptation. The proposed algorithm is applied on scalar problems to compute the solution with discontinuity or boundary layer. Presented numerical results show underlying second order schemes approximate discontinuities and boundary layers without spurious oscillations. |
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Keywords: | data dependent stability evolutionary equations finite difference schemes mesh adaptation modified equation analysis |
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