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1_quadrature.html

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     <title>1. Numerical quadrature &#8212; Finite element course 2024.0 documentation</title>
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@@ -52,11 +52,7 @@
 <span id="quadrature"></span><h1><span class="section-number">1. </span>Numerical quadrature<a class="headerlink" href="#numerical-quadrature" title="Link to this heading">¶</a></h1>
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@@ -117,11 +113,7 @@ <h2><span class="section-number">1.1. </span>Exact and incomplete quadrature<a c
 <h2><span class="section-number">1.2. </span>Examples in one dimension<a class="headerlink" href="#examples-in-one-dimension" title="Link to this heading">¶</a></h2>
 <details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3">
 <summary class="sd-summary-title sd-card-header">
-A video recording of the following material is available here.<div class="sd-summary-down docutils">
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-</summary><div class="sd-summary-content sd-card-body docutils">
+<span class="sd-summary-text">A video recording of the following material is available here.</span><span class="sd-summary-state-marker sd-summary-chevron-right"><svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-right" viewBox="0 0 24 24" aria-hidden="true"><path d="M8.72 18.78a.75.75 0 0 1 0-1.06L14.44 12 8.72 6.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018l6.25 6.25a.75.75 0 0 1 0 1.06l-6.25 6.25a.75.75 0 0 1-1.06 0Z"></path></svg></span></summary><div class="sd-summary-content sd-card-body docutils">
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@@ -150,11 +142,7 @@ <h2><span class="section-number">1.2. </span>Examples in one dimension<a class="
 <h2><span class="section-number">1.3. </span>Reference cells<a class="headerlink" href="#reference-cells" title="Link to this heading">¶</a></h2>
 <details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3">
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-A video recording of the following material is available here.<div class="sd-summary-down docutils">
-<svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-down" viewBox="0 0 24 24" aria-hidden="true"><path fill-rule="evenodd" d="M5.22 8.72a.75.75 0 000 1.06l6.25 6.25a.75.75 0 001.06 0l6.25-6.25a.75.75 0 00-1.06-1.06L12 14.44 6.28 8.72a.75.75 0 00-1.06 0z"></path></svg></div>
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-</summary><div class="sd-summary-content sd-card-body docutils">
+<span class="sd-summary-text">A video recording of the following material is available here.</span><span class="sd-summary-state-marker sd-summary-chevron-right"><svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-right" viewBox="0 0 24 24" aria-hidden="true"><path d="M8.72 18.78a.75.75 0 0 1 0-1.06L14.44 12 8.72 6.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018l6.25 6.25a.75.75 0 0 1 0 1.06l-6.25 6.25a.75.75 0 0 1-1.06 0Z"></path></svg></span></summary><div class="sd-summary-content sd-card-body docutils">
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@@ -260,7 +248,8 @@ <h3><span class="section-number">1.3.2. </span>Reference cell entities<a class="
 <iframe allowfullscreen="true" src="https://www.youtube.com/embed/7A7JU7bGw0E?modestbranding=1;controls=0;rel=0" style="border: 0; height: 367px; width: 600px">
 </iframe></div></div>
 <figure class="align-default" id="id4">
-<span id="figreferenceentities"></span><a class="reference internal image-reference" href="_images/entities.svg"><img alt="_images/entities.svg" src="_images/entities.svg" width="50%" /></a>
+<span id="figreferenceentities"></span><a class="reference internal image-reference" href="_images/entities.svg"><img alt="_images/entities.svg" src="_images/entities.svg" style="width: 50%;" />
+</a>
 <figcaption>
 <p><span class="caption-number">Fig. 1.5 </span><span class="caption-text">Local numbering and orientation of the reference entities.</span><a class="headerlink" href="#id4" title="Link to this image">¶</a></p>
 </figcaption>
@@ -282,11 +271,7 @@ <h3><span class="section-number">1.3.2. </span>Reference cell entities<a class="
 <h2><span class="section-number">1.4. </span>Quadrature rules on reference elements<a class="headerlink" href="#quadrature-rules-on-reference-elements" title="Link to this heading">¶</a></h2>
 <details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3">
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-A video recording of the following material is available here.<div class="sd-summary-down docutils">
-<svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-down" viewBox="0 0 24 24" aria-hidden="true"><path fill-rule="evenodd" d="M5.22 8.72a.75.75 0 000 1.06l6.25 6.25a.75.75 0 001.06 0l6.25-6.25a.75.75 0 00-1.06-1.06L12 14.44 6.28 8.72a.75.75 0 00-1.06 0z"></path></svg></div>
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+<span class="sd-summary-text">A video recording of the following material is available here.</span><span class="sd-summary-state-marker sd-summary-chevron-right"><svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-right" viewBox="0 0 24 24" aria-hidden="true"><path d="M8.72 18.78a.75.75 0 0 1 0-1.06L14.44 12 8.72 6.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018l6.25 6.25a.75.75 0 0 1 0 1.06l-6.25 6.25a.75.75 0 0 1-1.06 0Z"></path></svg></span></summary><div class="sd-summary-content sd-card-body docutils">
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@@ -349,7 +334,8 @@ <h2><span class="section-number">1.6. </span>Extending Legendre-Gauß quadrature
 <span class="eqno">(1.12)<a class="headerlink" href="#equation-1-quadrature-4" title="Link to this equation">¶</a></span>\[(x_\textrm{tri},\ y_\textrm{tri}) =
   \left(x_\textrm{sq},\ y_\textrm{sq}(1 - x_\textrm{sq})\right)\]</div>
 <figure class="align-default" id="id5">
-<span id="figduffy"></span><a class="reference internal image-reference" href="_images/duffy.svg"><img alt="_images/duffy.svg" src="_images/duffy.svg" width="60%" /></a>
+<span id="figduffy"></span><a class="reference internal image-reference" href="_images/duffy.svg"><img alt="_images/duffy.svg" src="_images/duffy.svg" style="width: 60%;" />
+</a>
 <figcaption>
 <p><span class="caption-number">Fig. 1.6 </span><span class="caption-text">The Duffy transform maps a square to a triangle by collapsing one side.</span><a class="headerlink" href="#id5" title="Link to this image">¶</a></p>
 </figcaption>
@@ -370,11 +356,7 @@ <h2><span class="section-number">1.6. </span>Extending Legendre-Gauß quadrature
 <h2><span class="section-number">1.7. </span>Implementing quadrature rules in Python<a class="headerlink" href="#implementing-quadrature-rules-in-python" title="Link to this heading">¶</a></h2>
 <details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3">
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-A video recording about how to do this exercise is available here.<div class="sd-summary-down docutils">
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+<span class="sd-summary-text">A video recording about how to do this exercise is available here.</span><span class="sd-summary-state-marker sd-summary-chevron-right"><svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-right" viewBox="0 0 24 24" aria-hidden="true"><path d="M8.72 18.78a.75.75 0 0 1 0-1.06L14.44 12 8.72 6.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018l6.25 6.25a.75.75 0 0 1 0 1.06l-6.25 6.25a.75.75 0 0 1-1.06 0Z"></path></svg></span></summary><div class="sd-summary-content sd-card-body docutils">
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@@ -408,19 +390,15 @@ <h2><span class="section-number">1.7. </span>Implementing quadrature rules in Py
 <p>You can implement
 <a class="reference internal" href="fe_utils.html#fe_utils.quadrature.QuadratureRule.integrate" title="fe_utils.quadrature.QuadratureRule.integrate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">integrate()</span></code></a> in one line
 using a <a class="reference external" href="https://docs.python.org/3/tutorial/datastructures.html#list-comprehensions">list
-comprehension</a> and <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dot.html#numpy.dot" title="(in NumPy v1.26)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.dot()</span></code></a>.</p>
+comprehension</a> and <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dot.html#numpy.dot" title="(in NumPy v2.2)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.dot()</span></code></a>.</p>
 </div>
 <div class="admonition hint">
 <p class="admonition-title">Hint</p>
 <p>Don’t forget to activate your Python venv!</p>
 </div>
 <details class="sd-sphinx-override sd-dropdown sd-card sd-mb-3">
 <summary class="sd-summary-title sd-card-header">
-A video recording of the solution to this exercise is available here.<div class="sd-summary-down docutils">
-<svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-down" viewBox="0 0 24 24" aria-hidden="true"><path fill-rule="evenodd" d="M5.22 8.72a.75.75 0 000 1.06l6.25 6.25a.75.75 0 001.06 0l6.25-6.25a.75.75 0 00-1.06-1.06L12 14.44 6.28 8.72a.75.75 0 00-1.06 0z"></path></svg></div>
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-<svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-up" viewBox="0 0 24 24" aria-hidden="true"><path fill-rule="evenodd" d="M18.78 15.28a.75.75 0 000-1.06l-6.25-6.25a.75.75 0 00-1.06 0l-6.25 6.25a.75.75 0 101.06 1.06L12 9.56l5.72 5.72a.75.75 0 001.06 0z"></path></svg></div>
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+<span class="sd-summary-text">A video recording of the solution to this exercise is available here.</span><span class="sd-summary-state-marker sd-summary-chevron-right"><svg version="1.1" width="1.5em" height="1.5em" class="sd-octicon sd-octicon-chevron-right" viewBox="0 0 24 24" aria-hidden="true"><path d="M8.72 18.78a.75.75 0 0 1 0-1.06L14.44 12 8.72 6.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018l6.25 6.25a.75.75 0 0 1 0 1.06l-6.25 6.25a.75.75 0 0 1-1.06 0Z"></path></svg></span></summary><div class="sd-summary-content sd-card-body docutils">
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@@ -439,7 +417,7 @@ <h2><span class="section-number">1.7. </span>Implementing quadrature rules in Py
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