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UID:news920@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20191104T081039
DTSTART;TZID=Europe/Zurich:20191108T110000
SUMMARY:Seminar in Numerical Analysis: Omar Lakkis (University of Sussex)
DESCRIPTION:Aposteriori error estimates provide a rigorous foundation for t
 he derivation of efficient adaptive algorithms for the approximation of so
 lutions of partial differential equations (PDEs).  While the literature i
 s rich with results for the approximation of elliptic and parabolic PDEs\,
  it is much less developed for the hyperbolic equations such as the acoust
 ic or elastic wave equations.  In this talk\, I will review some of the "
 standard" aposteriori results for the scalar linear wave equation\, includ
 ing those of [1] and [2]\, and present recent improvements and further dev
 elopments to lower order Sobolev norms based on Baker’s Trick [3] for ba
 ckward Euler schemes.  Subsequent focus will be given to practically rele
 vant methods such as Verlet\, Cosine\, or Newmark methods\, a popular exam
 ple of which is the Leap-frog method [4].\\r\\nNotes: This is based on joi
 nt work with E.H. Georgoulis\, C. Makridakis and J.M. Virtanen.\\r\\nRefer
 ences:\\r\\n[1] W. Bangerth and R. Rannacher\, J. Comput. Acoust. 9(2):575
 –591\, 2001.[2] C. Bernardi and E. Süli\, Math. Models Methods Appl. Sc
 i. 15(2):199--225\, 2005.[3] E. H. Georgoulis\, O. Lakkis\, and C. Makrida
 kis. IMA J. Numer. Anal.\, 33(4):1245–1264\, 2013\, http://arxiv.org/abs
 /1003.3641[4] E. H. Georgoulis\, O. Lakkis\, C. Makridakis\, and J. M. Vir
 tanen. SIAM J. Numer. Anal.\, 54(1)\, 2016\, http://arxiv.org/abs/1411.757
 2 \\r\\nFor further information about the seminar\, please visit this web
 page [t3://page?uid=1115].
X-ALT-DESC:<p>Aposteriori error estimates provide a rigorous foundation for
  the derivation of efficient adaptive algorithms for the approximation of 
 solutions of partial differential equations (PDEs). &nbsp\;While the liter
 ature is rich with results for the approximation of elliptic and parabolic
  PDEs\, it is much less developed for the hyperbolic equations such as the
  acoustic or elastic wave equations. &nbsp\;In this talk\, I will review s
 ome of the &quot\;standard&quot\; aposteriori results for the scalar linea
 r wave equation\, including those of [1] and [2]\, and present recent impr
 ovements and further developments to lower order Sobolev norms based on Ba
 ker’s Trick [3] for backward Euler schemes. &nbsp\;Subsequent focus will
  be given to practically relevant methods such as Verlet\, Cosine\, or New
 mark methods\, a popular example of which is the Leap-frog method [4].</p>
 \n<p><br />Notes: This is based on joint work with E.H. Georgoulis\, C. Ma
 kridakis and J.M. Virtanen.<br /></p>\n<p>References:</p>\n<p>[1] W. Bange
 rth and R. Rannacher\, J. Comput. Acoust. 9(2):575–591\, 2001.<br />[2] 
 C. Bernardi and E. Süli\, Math. Models Methods Appl. Sci. 15(2):199--225\
 , 2005.<br />[3] E. H. Georgoulis\, O. Lakkis\, and C. Makridakis. IMA J. 
 Numer. Anal.\, 33(4):1245–1264\, 2013\, http://arxiv.org/abs/1003.3641<b
 r />[4] E. H. Georgoulis\, O. Lakkis\, C. Makridakis\, and J. M. Virtanen.
  SIAM J. Numer. Anal.\, 54(1)\, 2016\, http://arxiv.org/abs/1411.7572 </p>
 \n<p>For further information about the seminar\, please visit this&nbsp\;<
 a href="t3://page?uid=1115" title="Opens internal link in current window" 
 class="internal-link">webpage</a>.</p>
DTEND;TZID=Europe/Zurich:20191108T120000
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