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Least‐squares finite element method on adaptive grid for PDEs with shocks
Author(s) -
Xue Jiaxing,
Liao Guojun
Publication year - 2006
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20087
Subject(s) - partial differential equation , finite element method , grid , shock (circulatory) , moving least squares , burgers' equation , nonlinear system , mathematics , adaptive mesh refinement , least squares function approximation , mathematical optimization , computer science , algorithm , mathematical analysis , geometry , computational science , structural engineering , physics , engineering , medicine , statistics , quantum mechanics , estimator
We apply the least‐squares finite element method with adaptive grid to nonlinear time‐dependent PDEs with shocks. The least‐squares finite element method is also used in applying the deformation method to generate the adaptive moving grids. The effectiveness of this method is demonstrated by solving a Burgers' equation with shocks. Computational results on uniform grids and adaptive grids are compared for the purpose of evaluation. The results show that the adaptive grids can capture the shock more sharply with significantly less computational time. For moving shock, the adaptive grid moves correctly with the shock. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006