پديد آورنده :
جمالي، مجيد
عنوان :
تجزيه و تحليل روش گالركين ناپيوسته براي معادله ي زير پخش
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
نه،118ص.: مصور،جدول،نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
مهدي تاتاري
استاد مشاور :
محمدرضا رئوفي
توصيفگر ها :
معادله سرسخت , انتگرال كسري ريمان - ليوويل
تاريخ نمايه سازي :
8/11/92
استاد داور :
رضا مختاري، داوود ميرزايي
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Analysis of a Discontinuous Galerkin method for sub di usion equation Majid Jamali majid jamali@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mehdi Tatari mtatari@cc iut ac ir Advisor Dr Mohammad Reza Raoo raoo @cc iut ac ir 2013 MSC 65M12 65M60 65M99 Keywords Discontinuous Galerkin method sub di usion equation sti equation Riemann Liouvillefractional integration Abstract This thesis consists of three chapters rst of which is about a class of nite element method and especially the Discontinuous Galerkin DG method for solving a boundary value problem in onedimension The DG method has been underrapid development recently and has found its use veryquickly in such diverse application as aeroacoustics semi conductor device simulation thurbomachin ery turbulent ows materials processing MHD and plasma simulations as well as image processing Although there has been a lot of interest from mathematician physicists and engineers applying DGmethod for their problem We study a fractional di usion equation involving a parameter in the range 1 0 where thefractional power is the Riemann Liouville sense The problem provides a macroscopic continuummodel of sub di usion with u giving the density of the di using particles that have mean squaredisplacement proportional to t1 In the limiting case 0 we have Brownian motion and u obeysthe classical heat equation In 27 McLean and Mustapha Kassem studied discontinuous Galerkin methods for the time dis cretization of problem in the case 0 1 and proving optimal error bounds for piecewise constantand piecewise linear trial functions The convergence analysis for the case 1 0 is more di cult In the second chapter we rst employ a piecewise constant discontinuous Galerkin method for the
استاد راهنما :
مهدي تاتاري
استاد مشاور :
محمدرضا رئوفي
استاد داور :
رضا مختاري، داوود ميرزايي
