91Й«ЗйЖ¬

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CATEGORIES:College of Arts and Sciences,College of Engineering,Thesis/Disse
 rtations
DESCRIPTION:°ХґЗ±иѕ±і¦:Мэ High-order Conservative Discontinuous Galerkin Methods
  via Implicit Penalization for the Generalized Korteweg--de Vries Equation
  and the Hirota--Satsuma KdV SystemAbstract: В  В В  We develop a new cons
 ervative discontinuous Galerkin (DG) methods for nonlinear wave problems, 
 focusing on the generalized KortewegвЂ“de Vries (gKdV) equation and the co
 upled HirotaвЂ“Satsuma KdV (HS-KdV) system. The proposed methods preserve 
 mass through the single-valued structure of numerical traces, while energy
  and Hamiltonian conservation are enforced by implicitly determining penal
 ty parameters in the numerical traces through auxiliary conservation const
 raints. In our previous work, we developed a conservative DG method for th
 e gKdV equation; however, that formulation involves the time derivative of
  the jump of the approximate solution, which complicates extensions beyond
  second-order temporal accuracy. Our new formulation overcomes this limita
 tion by introducing a redesigned trace configuration that eliminates the d
 erivative-of-jump term. This novel enhancement seamlessly paves the way fo
 r higher-order time discretizations and requires solving fewer nonlinear s
 ystems per time step than the previous approach. For the coupled HS-KdV sy
 stem, we present the first conservative DG method capable of preserving al
 l three invariants of the exact solution. Numerical results demonstrate th
 e accuracy and expected convergence behavior of the proposed methods, as w
 ell as long-time stability and strong conservation properties for both the
  gKdV equation and HS- KdV system.В  ADVISOR(s): В  В  В  В  В  В  В  В  
 В  В  В  В  В   Dr. Bo Dong, Department of Mathematics (bdong@umassd.edu) 
 Dr. Yanlai Chen, Chief Research Officer (yanlai.chen@umassd.edu)  COMMITTE
 E MEMBERS:  Dr. Zheng Chen, Department of Mathematics Dr. Mazdak Tootkabon
 i, Department of Civil and Environmental Engineering  NOTE:В  All EAS Stud
 ents are ENCOURAGED to attend.\nEvent page: /events/
 cms/eas-doctoral-proposal-defense--by-muhammad-shan-tariq.php
X-ALT-DESC;FMTTYPE=text/html:<html><Body><h1><a href="/">91Й«ЗйЖ¬</a></h1><script>
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</script><p>°ХґЗ±иѕ±і¦:Мэ</p>\n<p>High-order Con
 servative Discontinuous Galerkin Methods via Implicit Penalization for the
  Generalized Korteweg--de Vries Equation and the Hirota--Satsuma KdV Syste
 mAbstract: В  В В </p>\n<p>We develop a new conservative discontinuous Gal
 erkin (DG) methods for nonlinear wave problems\, focusing on the generaliz
 ed KortewegвЂ“de Vries (gKdV) equation and the coupled HirotaвЂ“Satsuma Kd
 V (HS-KdV) system. The proposed methods preserve mass through the single-v
 alued structure of numerical traces\, while energy and Hamiltonian conserv
 ation are enforced by implicitly determining penalty parameters in the num
 erical traces through auxiliary conservation constraints. In our previous 
 work\, we developed a conservative DG method for the gKdV equation\; howev
 er\, that formulation involves the time derivative of the jump of the appr
 oximate solution\, which complicates extensions beyond second-order tempor
 al accuracy. Our new formulation overcomes this limitation by introducing 
 a redesigned trace configuration that eliminates the derivative-of-jump te
 rm. This novel enhancement seamlessly paves the way for higher-order time 
 discretizations and requires solving fewer nonlinear systems per time step
  than the previous approach. For the coupled HS-KdV system\, we present th
 e first conservative DG method capable of preserving all three invariants 
 of the exact solution. Numerical results demonstrate the accuracy and expe
 cted convergence behavior of the proposed methods\, as well as long-time s
 tability and strong conservation properties for both the gKdV equation and
  HS- KdV system.В </p>\n<p>ADVISOR(s): В  В  В  В  В  В  В  В  В  В  В  В 
  В </p>\n<ul>\n<li>Dr. Bo Dong\, Department of Mathematics (bdong@umassd.e
 du)</li>\n<li>Dr. Yanlai Chen\, Chief Research Officer (yanlai.chen@umassd
 .edu)</li>\n</ul>\n<p>COMMITTEE MEMBERS:</p>\n<ul>\n<li>Dr. Zheng Chen\, D
 epartment of Mathematics</li>\n<li>Dr. Mazdak Tootkaboni\, Department of C
 ivil and Environmental Engineering</li>\n</ul>\n<p>NOTE:В  All EAS Student
 s are ENCOURAGED to attend.</p><p>Event page: </a></p></body></html>
DTSTAMP:20260518T220417
DTSTART;TZID=America/New_York:20260528T093000
DTEND;TZID=America/New_York:20260528T110000
LOCATION:TXT 105 - CSCDR
SUMMARY;LANGUAGE=en-us:EAS Doctoral Proposal Defense  by Muhammad Shan Tari
 q
UID:f20a203c90b3ab6eeb4145b96abd834f@www.umassd.edu
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