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95 changes: 48 additions & 47 deletions basix/main/index.html
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Expand Up @@ -124,7 +124,8 @@ <h2 id="project_subtitle"><a class='fenicsnav' href='https://docs.fenicsproject.
&nbsp;
<a class='fenicsnav' href='https://docs.fenicsproject.org/basix/main/python'>Python docs</a>
</h2><p><a href="https://github.com/FEniCS/basix/actions/workflows/pythonapp.yml"><img alt="Basix CI" src="https://github.com/FEniCS/basix/actions/workflows/pythonapp.yml/badge.svg" /></a>
<a href="https://github.com/FEniCS/basix/actions/workflows/spack.yml"><img alt="Spack install" src="https://github.com/FEniCS/basix/actions/workflows/spack.yml/badge.svg" /></a></p>
<a href="https://github.com/FEniCS/basix/actions/workflows/spack.yml"><img alt="Spack install" src="https://github.com/FEniCS/basix/actions/workflows/spack.yml/badge.svg" /></a>
<a href="https://defelement.org/verification.html"><img alt="DefElement verification" src="https://defelement.org/badges/basix.ufl.svg" /></a></p>
<p>Basix is a finite element definition and tabulation runtime library.
Basix allows users to:</p>
<ul>
Expand Down Expand Up @@ -159,94 +160,94 @@ <h3>Interval</h3>
<p><img alt="The numbering of a reference interval" src="img/interval_numbering.png" /></p>
<p>The following elements are supported on an interval:</p>
<ul>
<li><a href="https://defelement.com/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.com/elements/bubble.html">Bubble</a></li>
<li><a href="https://defelement.com/elements/serendipity.html">Serendipity</a></li>
<li><a href="https://defelement.com/elements/hermite.html">Hermite</a></li>
<li><a href="https://defelement.com/elements/p1-iso-p2.html">iso</a></li>
<li><a href="https://defelement.org/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.org/elements/bubble.html">Bubble</a></li>
<li><a href="https://defelement.org/elements/serendipity.html">Serendipity</a></li>
<li><a href="https://defelement.org/elements/hermite.html">Hermite</a></li>
<li><a href="https://defelement.org/elements/p1-iso-p2.html">iso</a></li>
</ul>
<h3>Triangle</h3>
<p>In Basix, the sub-entities of the reference triangle are numbered as
follows:</p>
<p><img alt="The numbering of a reference triangle" src="img/triangle_numbering.png" /></p>
<p>The following elements are supported on a triangle:</p>
<ul>
<li><a href="https://defelement.com/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.com/elements/nedelec1.html">N&eacute;d&eacute;lec first kind</a></li>
<li><a href="https://defelement.com/elements/raviart-thomas.html">Raviart-Thomas</a></li>
<li><a href="https://defelement.com/elements/nedelec2.html">N&eacute;d&eacute;lec second kind</a></li>
<li><a href="https://defelement.com/elements/brezzi-douglas-marini.html">Brezzi-Douglas-Marini</a></li>
<li><a href="https://defelement.com/elements/regge.html">Regge</a></li>
<li><a href="https://defelement.com/elements/hellan-hermann-johnson.html">Hellan-Herrmann-Johnson</a></li>
<li><a href="https://defelement.com/elements/crouzeix-raviart.html">Crouzeix-Raviart</a></li>
<li><a href="https://defelement.com/elements/bubble.html">Bubble</a></li>
<li><a href="https://defelement.com/elements/hermite.html">Hermite</a></li>
<li><a href="https://defelement.com/elements/p1-iso-p2.html">iso</a></li>
<li><a href="https://defelement.org/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.org/elements/nedelec1.html">N&eacute;d&eacute;lec first kind</a></li>
<li><a href="https://defelement.org/elements/raviart-thomas.html">Raviart-Thomas</a></li>
<li><a href="https://defelement.org/elements/nedelec2.html">N&eacute;d&eacute;lec second kind</a></li>
<li><a href="https://defelement.org/elements/brezzi-douglas-marini.html">Brezzi-Douglas-Marini</a></li>
<li><a href="https://defelement.org/elements/regge.html">Regge</a></li>
<li><a href="https://defelement.org/elements/hellan-hermann-johnson.html">Hellan-Herrmann-Johnson</a></li>
<li><a href="https://defelement.org/elements/crouzeix-raviart.html">Crouzeix-Raviart</a></li>
<li><a href="https://defelement.org/elements/bubble.html">Bubble</a></li>
<li><a href="https://defelement.org/elements/hermite.html">Hermite</a></li>
<li><a href="https://defelement.org/elements/p1-iso-p2.html">iso</a></li>
</ul>
<h3>Quadrilateral</h3>
<p>In Basix, the sub-entities of the reference quadrilateral are numbered
as follows:</p>
<p><img alt="The numbering of a reference quadrilateral" src="img/quadrilateral_numbering.png" /></p>
<p>The following elements are supported on a quadrilateral:</p>
<ul>
<li><a href="https://defelement.com/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.com/elements/nedelec1.html">N&eacute;d&eacute;lec first kind</a></li>
<li><a href="https://defelement.com/elements/qdiv.html">Raviart-Thomas</a></li>
<li><a href="https://defelement.com/elements/scurl.html">N&eacute;d&eacute;lec second kind</a></li>
<li><a href="https://defelement.com/elements/sdiv.html">Brezzi-Douglas-Marini</a></li>
<li><a href="https://defelement.com/elements/bubble.html">Bubble</a></li>
<li><a href="https://defelement.com/elements/dpc.html">DPC</a></li>
<li><a href="https://defelement.com/elements/serendipity.html">Serendipity</a></li>
<li><a href="https://defelement.com/elements/p1-iso-p2.html">iso</a></li>
<li><a href="https://defelement.org/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.org/elements/nedelec1.html">N&eacute;d&eacute;lec first kind</a></li>
<li><a href="https://defelement.org/elements/qdiv.html">Raviart-Thomas</a></li>
<li><a href="https://defelement.org/elements/scurl.html">N&eacute;d&eacute;lec second kind</a></li>
<li><a href="https://defelement.org/elements/sdiv.html">Brezzi-Douglas-Marini</a></li>
<li><a href="https://defelement.org/elements/bubble.html">Bubble</a></li>
<li><a href="https://defelement.org/elements/dpc.html">DPC</a></li>
<li><a href="https://defelement.org/elements/serendipity.html">Serendipity</a></li>
<li><a href="https://defelement.org/elements/p1-iso-p2.html">iso</a></li>
</ul>
<h3>Tetrahedron</h3>
<p>In Basix, the sub-entities of the reference tetrahedron are numbered as
follows:</p>
<p><img alt="The numbering of a reference tetrahedron" src="img/tetrahedron_numbering.png" /></p>
<p>The following elements are supported on a tetrahedron:</p>
<ul>
<li><a href="https://defelement.com/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.com/elements/nedelec1.html">N&eacute;d&eacute;lec first kind</a></li>
<li><a href="https://defelement.com/elements/raviart-thomas.html">Raviart-Thomas</a></li>
<li><a href="https://defelement.com/elements/nedelec2.html">N&eacute;d&eacute;lec second kind</a></li>
<li><a href="https://defelement.com/elements/brezzi-douglas-marini.html">Brezzi-Douglas-Marini</a></li>
<li><a href="https://defelement.com/elements/regge.html">Regge</a></li>
<li><a href="https://defelement.com/elements/crouzeix-raviart.html">Crouzeix-Raviart</a></li>
<li><a href="https://defelement.com/elements/bubble.html">Bubble</a></li>
<li><a href="https://defelement.com/elements/hermite.html">Hermite</a></li>
<li><a href="https://defelement.com/elements/p1-iso-p2.html">iso</a></li>
<li><a href="https://defelement.org/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.org/elements/nedelec1.html">N&eacute;d&eacute;lec first kind</a></li>
<li><a href="https://defelement.org/elements/raviart-thomas.html">Raviart-Thomas</a></li>
<li><a href="https://defelement.org/elements/nedelec2.html">N&eacute;d&eacute;lec second kind</a></li>
<li><a href="https://defelement.org/elements/brezzi-douglas-marini.html">Brezzi-Douglas-Marini</a></li>
<li><a href="https://defelement.org/elements/regge.html">Regge</a></li>
<li><a href="https://defelement.org/elements/crouzeix-raviart.html">Crouzeix-Raviart</a></li>
<li><a href="https://defelement.org/elements/bubble.html">Bubble</a></li>
<li><a href="https://defelement.org/elements/hermite.html">Hermite</a></li>
<li><a href="https://defelement.org/elements/p1-iso-p2.html">iso</a></li>
</ul>
<h3>Hexahedron</h3>
<p>In Basix, the sub-entities of the reference hexahedron are numbered as
follows:</p>
<p><img alt="The numbering of a reference hexahedron" src="img/hexahedron_numbering.png" /></p>
<p>The following elements are supported on a hexahedron:</p>
<ul>
<li><a href="https://defelement.com/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.com/elements/nedelec1.html">N&eacute;d&eacute;lec first kind</a></li>
<li><a href="https://defelement.com/elements/qdiv.html">Raviart-Thomas</a></li>
<li><a href="https://defelement.com/elements/scurl.html">N&eacute;d&eacute;lec second kind</a></li>
<li><a href="https://defelement.com/elements/sdiv.html">Brezzi-Douglas-Marini</a></li>
<li><a href="https://defelement.com/elements/bubble.html">Bubble</a></li>
<li><a href="https://defelement.com/elements/dpc.html">DPC</a></li>
<li><a href="https://defelement.com/elements/serendipity.html">Serendipity</a></li>
<li><a href="https://defelement.com/elements/p1-iso-p2.html">iso</a></li>
<li><a href="https://defelement.org/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.org/elements/nedelec1.html">N&eacute;d&eacute;lec first kind</a></li>
<li><a href="https://defelement.org/elements/qdiv.html">Raviart-Thomas</a></li>
<li><a href="https://defelement.org/elements/scurl.html">N&eacute;d&eacute;lec second kind</a></li>
<li><a href="https://defelement.org/elements/sdiv.html">Brezzi-Douglas-Marini</a></li>
<li><a href="https://defelement.org/elements/bubble.html">Bubble</a></li>
<li><a href="https://defelement.org/elements/dpc.html">DPC</a></li>
<li><a href="https://defelement.org/elements/serendipity.html">Serendipity</a></li>
<li><a href="https://defelement.org/elements/p1-iso-p2.html">iso</a></li>
</ul>
<h3>Prism</h3>
<p>In Basix, the sub-entities of the reference prism are numbered as
follows:</p>
<p><img alt="The numbering of a reference prism" src="img/prism_numbering.png" /></p>
<p>The following elements are supported on a prism:</p>
<ul>
<li><a href="https://defelement.com/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.org/elements/lagrange.html">Lagrange</a></li>
</ul>
<h3>Pyramid</h3>
<p>In Basix, the sub-entities of the reference pyramid are numbered as
follows:</p>
<p><img alt="The numbering of a reference pyramid" src="img/pyramid_numbering.png" /></p>
<p>The following elements are supported on a pyramid:</p>
<ul>
<li><a href="https://defelement.com/elements/lagrange.html">Lagrange</a></li>
<li><a href="https://defelement.org/elements/lagrange.html">Lagrange</a></li>
</ul>

</section>
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Expand Up @@ -202,7 +202,7 @@ Degree 1 Ravairt--Thomas element

As a second example, we create a degree 1 Raviart--Thomas element on a triangle. Details of
the definition of this element can be found at
https://defelement.com/elements/raviart-thomas.html. This element
https://defelement.org/elements/raviart-thomas.html. This element
spans:

.. math::
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Expand Up @@ -22,7 +22,7 @@ Conforming CR element on a triangle
We begin by implementing this element on a triangle. The following function
implements this element for an arbitrary degree. Details of the definition of
this element can be found at
https://defelement.com/elements/conforming-crouzeix-raviart.html.
https://defelement.org/elements/conforming-crouzeix-raviart.html.

As the input to this function, we use the degree of the element as shown on
DefElement. For most degrees, the highest degree polynomial in this elements
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Expand Up @@ -326,7 +326,7 @@ <h3>Creating the element<a class="headerlink" href="#creating-the-element" title
<h2>Degree 1 Ravairt–Thomas element<a class="headerlink" href="#degree-1-ravairt-thomas-element" title="Link to this heading"></a></h2>
<p>As a second example, we create a degree 1 Raviart–Thomas element on a triangle. Details of
the definition of this element can be found at
<a class="reference external" href="https://defelement.com/elements/raviart-thomas.html">https://defelement.com/elements/raviart-thomas.html</a>. This element
<a class="reference external" href="https://defelement.org/elements/raviart-thomas.html">https://defelement.org/elements/raviart-thomas.html</a>. This element
spans:</p>
<div class="math notranslate nohighlight">
\[\left\{(1, 0),\; (0, 1),\; (x, y)\right\}.\]</div>
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Expand Up @@ -174,7 +174,7 @@ <h2>Conforming CR element on a triangle<a class="headerlink" href="#conforming-c
<p>We begin by implementing this element on a triangle. The following function
implements this element for an arbitrary degree. Details of the definition of
this element can be found at
<a class="reference external" href="https://defelement.com/elements/conforming-crouzeix-raviart.html">https://defelement.com/elements/conforming-crouzeix-raviart.html</a>.</p>
<a class="reference external" href="https://defelement.org/elements/conforming-crouzeix-raviart.html">https://defelement.org/elements/conforming-crouzeix-raviart.html</a>.</p>
<p>As the input to this function, we use the degree of the element as shown on
DefElement. For most degrees, the highest degree polynomial in this elements
polynomial space is actually one degree higher, so we pass <cite>degree + 1</cite> into
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