An estimate of accuracy for interpolant numerical solutions of a PDE problem
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2004
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| _version_ | 1866914099083870208 |
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| author | Argentini, Gianluca |
| author_facet | Argentini, Gianluca |
| contents | In this paper we present an estimate of accuracy for a piecewise polynomial approximation of a classical numerical solution to a non linear differential problem. We suppose the numerical solution U is computed using a grid with a small linear step and interval time Tu, while the polynomial approximation V is an interpolation of the values of a numerical solution on a less fine grid and interval time Tv << Tu. The estimate shows that the interpolant solution V can be, under suitable hypotheses, a good approximation and in general its computational cost is much lower of the cost of the fine numerical solution. We present two possible applications to linear case and periodic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_cs_0412120 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | An estimate of accuracy for interpolant numerical solutions of a PDE problem Argentini, Gianluca Numerical Analysis Mathematical Physics G.1.8 In this paper we present an estimate of accuracy for a piecewise polynomial approximation of a classical numerical solution to a non linear differential problem. We suppose the numerical solution U is computed using a grid with a small linear step and interval time Tu, while the polynomial approximation V is an interpolation of the values of a numerical solution on a less fine grid and interval time Tv << Tu. The estimate shows that the interpolant solution V can be, under suitable hypotheses, a good approximation and in general its computational cost is much lower of the cost of the fine numerical solution. We present two possible applications to linear case and periodic case. |
| title | An estimate of accuracy for interpolant numerical solutions of a PDE problem |
| topic | Numerical Analysis Mathematical Physics G.1.8 |
| url | https://arxiv.org/abs/cs/0412120 |