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81.
Viscoelastic flows remain a demanding class of problems for approximate analysis, particularly at increasing Weissenberg numbers. Part of the difficulty stems from the convective behavior and in the treatment of the stress field as a primary unknown. This latter aspect has led to the use of higher-order piecewise approximations for the stress approximation spaces in recent finite element research. The computational complexity of the discretized problem is increased significantly by this approach but at present it appears the most viable technique for solving these problems. Motivated by recent success in treating mixed systems and convective problems, we formulate here a least squares finite element method for the viscoelastic flow problem. Numerical experiments are conducted to test the method and examine its strengths and limitations. Some difficulties and open issues are identified through the numerical experiments. We consider the use of high degree elements (p refinement) to improve performance and accuracy. 相似文献
82.
83.
A new class of positivity‐preserving, flux‐limited finite‐difference and Petrov–Galerkin (PG) finite‐element methods are devised for reactive transport problems.The methods are similar to classical TVD flux‐limited schemes with the main difference being that the flux‐limiter constraint is designed to preserve positivity for problems involving diffusion and reaction. In the finite‐element formulation, we also consider the effect of numerical quadrature in the lumped and consistent mass matrix forms on the positivity‐preserving property. Analysis of the latter scheme shows that positivity‐preserving solutions of the resulting difference equations can only be guaranteed if the flux‐limited scheme is both implicit and satisfies an additional lower‐bound condition on time‐step size. We show that this condition also applies to standard Galerkin linear finite‐element approximations to the linear diffusion equation. Numerical experiments are provided to demonstrate the behavior of the methods and confirm the theoretical conditions on time‐step size, mesh spacing, and flux limiting for transport problems with and without nonlinear reaction. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
84.
Fisher's equation is a classical diffusion–reaction type of problem describing diffusion and nonlinear reproduction of a species. In the present study we develop a least-squares finite element formulation of Fisher's equation and carry out supporting numerical studies. Of particular interest are questions associated with the approximation of progressive wave solutions with minimum speed and the viability of the least-squares approach for this class of problem. © 1995 John Wiley & Sons, Inc. 相似文献
85.
Abe F Amidei D Apollinari G Atac M Auchincloss P Baden AR Bacchetta N Bailey MW Bamberger A Barnett BA Barbaro-Galtieri A Barnes VE Baumann T Bedeschi F Behrends S Belforte S Bellettini G Bellinger J Bensinger J Beretvas A Berge JP Bertolucci S Bhadra S Binkley M Blair R Blocker C Bolognesi V Booth AW Boswell C Brandenburg G Brown D Buckley-Geer E Budd HS Busetto G Byon-Wagner A Byrum KL Campagnari C Campbell M Carey R Carithers W Carlsmith D Carroll JT Cashmore R Castro A Cervelli F Chadwick K 《Physical review letters》1991,67(24):3351-3355
86.
Abe F Amidei D Apollinari G Atac M Auchincloss P Baden AR Bamberger A Barnett BA Barbaro-Galtieri A Barnes VE Bedeschi F Behrends S Belforte S Bellettini G Bellinger J Bensinger J Beretvas A Berge JP Bertolucci S Bhadra S Binkley M Blair R Blocker C Bolognesi V Booth AW Boswell C Brandenburg G Brown D Buckley E Budd HS Byon A Byrum KL Campagnari C Campbell M Carey R Carithers W Carlsmith D Carroll JT Cashmore R Cervelli F Chadwick K Chiarelli G Chinowsky W Cihangir S Clark AG Connor D 《Physical review letters》1991,66(23):2951-2955
87.
88.
Abe F Amidei D Apollinari G Ascoli G Atac M Auchincloss P Baden AR Barbaro-Galtieri A Barnes VE Bedeschi F Behrends S Belforte S Bellettini G Bellinger J Bensinger J Beretvas A Berge P Bertolucci S Bhadra S Binkley M Blair R Blocker C Bofill J Bolognesi V Booth AW Brandenburg G Brown D Byon A Byrum KL Campbell M Carey R Carithers W Carlsmith D Carroll JT Cashmore R Cervelli F Chadwick K Chapin T Chiarelli G Chinowsky W Cihangir S Cline D Connor D Contreras M Cooper J Cordelli M Curatolo M Day C 《Physical review D: Particles and fields》1991,44(3):601-616
89.
Abe F Amidei D Apollinari G Atac M Auchincloss P Baden AR Bamberger A Barbaro-Galtieri A Barnes VE Bedeschi F Behrends S Belforte S Bellettini G Bellinger J Bensinger J Beretvas A Berge JP Bertolucci S Bhadra S Binkley M Blair R Blocker C Booth AW Brandenburg G Brown D Buckley E Byon A Byrum KL Campagnari C Campbell M Carey R Carithers W Carlsmith D Carroll JT Cashmore R Cervelli F Chadwick K Chiarelli G Chinowsky W Cihangir S Clark AG Connor D Contreras M Cooper J Cordelli M Crane D Curatolo M 《Physical review D: Particles and fields》1991,43(3):664-686
90.
Abe F Amidei D Apollinari G Atac M Auchincloss P Baden AR Bamberger A Barbaro-Galtieri A Barnes VE Bedeschi F Behrends S Belforte S Bellettini G Bellinger J Bensinger J Beretvas A Berge JP Bertolucci S Bhadra S Binkley M Blair R Blocker C Booth AW Brandenburg G Brown D Buckley E Byon A Byrum KL Campagnari C Campbell M Carey R Carithers W Carlsmith D Carroll JT Cashmore R Cervelli F Chadwick K Chiarelli G Chinowsky W Cihangir S Clark AG Connor D Contreras M Cooper J Cordelli M Crane D Curatolo M 《Physical review D: Particles and fields》1991,44(1):29-52