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    <div class="moz-text-html" lang="x-unicode"> On 08/24/2016 11:27 AM,
      Andrew Ho wrote:<br>
      <blockquote
cite="mid:CADhXwgsAtKBsKx21djG44wqE_pX8a2hK0CcOXafXQ-ok+hDTnA@mail.gmail.com"
        type="cite">
        <div dir="ltr">Good geometric accuracy is very import for
          achieving appropriate convergence rates in complex geometry,
          not just using higher order polynomials on flat elements.<br>
          <div><br>
          </div>
          <div>If you look at Hesthaven's book Nodal Discontinuous
            Galerkin Methods, Table 9.1 shows that without support for
            curved elements, higher order DG element on flat elements
            converges at sub optimal rates due to inaccuracies produced
            by the boundary conditions.</div>
          <div><br>
          </div>
          <div>There's no way to re-construct this curved information
            correctly after the fact; it must be generated by the
            meshing software.</div>
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        <div class="gmail_extra"><br>
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      <br>
      I don't *entirely* agree with the suggestion the mesh generator
      has to provide that information. Some people reconstruct splines
      through the nodes to create higher order meshes after the fact
      (which also requires some detection or specification of sharp
      corners to break the spline). I personally take the given mesh
      from the generator in addition to an IGES/NURBS type CAD file for
      complex geometries, and then do a kind of projection for sub-cell
      curved boundary faces.<br>
      <br>
      <br>
      <blockquote
cite="mid:CADhXwgsAtKBsKx21djG44wqE_pX8a2hK0CcOXafXQ-ok+hDTnA@mail.gmail.com"
        type="cite">
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          <div class="gmail_quote">On Wed, Aug 24, 2016 at 10:12 AM, Jed
            Brown <span dir="ltr"><<a moz-do-not-send="true"
                href="mailto:jed@jedbrown.org" target="_blank">jed@jedbrown.org</a>></span>
            wrote:<br>
            <blockquote class="gmail_quote" style="margin:0 0 0
              .8ex;border-left:1px #ccc solid;padding-left:1ex"><span
                class="">Matthew Knepley <<a moz-do-not-send="true"
                  href="mailto:knepley@gmail.com">knepley@gmail.com</a>>

                writes:<br>
                >> Yes, I do not support that since I think its a
                crazy way to talk about<br>
                >> things. All the topological information is in
                the Tri3 mesh, and<br>
                >> Cubit has no business telling me about the
                function space.<br>
                >><br>
                >><br>
                >> Do you support / plan to support curved
                elements?<br>
                >><br>
                ><br>
                > I had "support" in there, but there were bugs. Toby
                and Mark discovered<br>
                > these, and Toby has fixed them. I think<br>
                > all of the fixes are in master now.<br>
                <br>
              </span>The context is clearly that the mesh generator
              needs to express the<br>
              curved elements.  DMPlex doesn't have a geometric model
              available, so it<br>
              doesn't know how to make the Tri3 elements curve to
              conform more<br>
              accurately to the boundary.  The mesh generator has no
              business telling<br>
              you what function space to use for your solution, but it'd
              be a shame to<br>
              prevent it from expressing element geometry.<br>
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          -- <br>
          <div class="gmail_signature" data-smartmail="gmail_signature">
            <div dir="ltr">Andrew Ho</div>
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