<div dir="ltr">Dear all,<div dir="auto"><br></div><div dir="auto">We remind you <b>today</b>'s<b> </b>appointment of the series of seminars "Insalate di Matematica".</div><div dir="auto">Here are the details:</div><div dir="auto"><br></div><div dir="auto"><u>Speaker</u>: <i>Manuel Trezzi</i> (Università degli Studi di Pavia)<br></div><div dir="auto"><br></div><div dir="auto"><div dir="auto"><span style="color:rgb(0,0,0)"><u>Date and time</u>: <b>17th of April 2024, 4:30 pm (CET)</b></span></div></div><div dir="auto"><br></div><div dir="auto"><div dir="auto"><font color="#000000"><u>Title</u>: </font><font color="#000000"><span style="background-color:rgb(255,229,153)">"</span></font><span style="background-color:rgb(255,229,153)">The Lightning Virtual Element Method</span><font color="#000000"><span style="background-color:rgb(255,229,153)">"</span></font></div><br></div><div dir="auto"><div dir="auto"><font color="#000000"><u>Abstract</u>:</font> The Virtual Element Method (VEM) is a method for discretizing partial
differential equations (PDEs) developed in 2013. This talk introduces
the Lightning Virtual Element Method (LVEM). This new VEM eliminates the
stabilization term by actually computing the basis functions using
rational functions. Thanks to the lightning Laplace solver by N.
Trefethen, the LVEM approximates the basis functions using rational
functions with poles clustered exponentially close to the corners of
each element of the polygonal tessellation. This results in two great
advantages. First, the mathematical analysis of a priori error estimates
is much easier and essentially identical to the one for any other
non-conforming Galerkin discretization. Second, the fact that the
lightning VEM computes the basis functions allows the user to access the
point-wise value of the numerical solution without needing any
reconstruction techniques. The cost of the local construction of the VEM
basis is the implementation price that one has to pay for the
advantages of the lightning VEM method, but the parallelizable nature of
this operation will ultimately result in a cost-efficient scheme
compared to standard VEM and FEM.</div><div dir="auto"><br></div><div dir="auto"><div dir="auto"><font color="#000000"><u>Keywords:</u></font> Virtual Element Method, Rational Functions, Stabilization free <div dir="auto"><br></div><div dir="auto"><br></div></div><div dir="auto"><div dir="auto"><u><b>Information to attend in room 3014</b></u></div><div dir="auto">The seminar will take place in room 3014, at the building U5-Ratio, Università degli Studi di Milano Bicocca.</div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto"><u><b>Information to attend online<br></b></u></div><div dir="auto"><div dir="auto"><a href="https://unimib.webex.com/unimib/j.php?MTID=m101728a0c0258813b6aa97783fb11fad" target="_blank">https://unimib.webex.com/unimib/j.php?MTID=m101728a0c0258813b6aa97783fb11fad</a> (password: insalate, 46725283 from phones)</div></div><div dir="auto"><div id="m_-4362650771707838389m_1557104255583827781m_-4439392858642327092m_5555831848437307896gmail-:183" style="direction:ltr;margin:8px 0px 0px;padding:0px;font-size:0.875rem;font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif"><div id="m_-4362650771707838389m_1557104255583827781m_-4439392858642327092m_5555831848437307896gmail-:17t" style="font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:small;line-height:1.5;font-family:Arial,Helvetica,sans-serif;overflow:hidden"><div dir="ltr"><div dir="auto"><div dir="auto"><div dir="auto"><div dir="auto"><br></div><div dir="auto">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at <a href="mailto:insalate.matematica@unimib.it" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">insalate.matematica@unimib.it</a>. Find us also on our Instagram page: <a href="https://www.instagram.com/insalate_di_matematica22/" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://www.instagram.com/insalate_di_matematica23/</a></div><div dir="auto"><br></div><div dir="auto"><div dir="auto"><font color="#000000">The organizers: Ettore Marmo, Simone Gallivanone, Fabio Mastrogiacomo, Marco Fusari, Tommaso Toti and Matteo Tarocchi.</font></div></div></div></div></div></div></div></div></div></div></div></div></div>