Spectral Element Method for Parabolic Initial Value Problem with Non-Smooth Data: Analysis and Application
| Autor: | Pravir Dutt, Chandra Shekhar Upadhyay, Arbaz Khan |
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| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Partial differential equation Applied Mathematics Spectral element method Mathematical analysis General Engineering Domain decomposition methods 010103 numerical & computational mathematics Function (mathematics) 01 natural sciences Theoretical Computer Science Exponential function 010101 applied mathematics Sobolev space Computational Mathematics Computational Theory and Mathematics Dimension (vector space) Initial value problem 0101 mathematics Software Mathematics |
| Zdroj: | Journal of Scientific Computing. 73:876-905 |
| ISSN: | 1573-7691 0885-7474 |
| DOI: | 10.1007/s10915-017-0457-0 |
| Popis: | In this paper, a least-squares spectral element method for parabolic initial value problem for two space dimension on parallel computers is presented. The theory is also valid for three dimension. This method gives exponential accuracy in both space and time. The method is based on minimization of residuals in terms of the partial differential equation and initial condition, in different Sobolev norms, and a term which measures the jump in the function and its derivatives across inter-element boundaries in appropriate fractional Sobolev norms. Rigorous error estimates for this method are given. Some specific numerical examples are solved to show the efficiency of this method. |
| Databáze: | OpenAIRE |
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