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FEniCS GitHub Actions committed Oct 11, 2024
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4 changes: 2 additions & 2 deletions dolfinx/main/cpp/demos/demo_biharmonic.html
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Expand Up @@ -136,8 +136,8 @@ <h3>Weak formulation<a class="headerlink" href="#weak-formulation" title="Link t
\forall \ K \in \mathcal{T} \right\}
\]</div>
<p>and considering the boundary conditions</p>
<div class="amsmath math notranslate nohighlight" id="equation-747fabe8-8a1c-4214-b7d9-8b88f33a0eb9">
<span class="eqno">(1)<a class="headerlink" href="#equation-747fabe8-8a1c-4214-b7d9-8b88f33a0eb9" title="Permalink to this equation"></a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-1ae86891-23be-4ba6-8b1c-84346d2775fc">
<span class="eqno">(1)<a class="headerlink" href="#equation-1ae86891-23be-4ba6-8b1c-84346d2775fc" title="Permalink to this equation"></a></span>\[\begin{align}
u &amp;= 0 \quad {\rm on} \ \partial\Omega, \\
\nabla^{2} u &amp;= 0 \quad {\rm on} \ \partial\Omega,
\end{align}\]</div>
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"cells": [
{
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"# Matrix-free conjugate gradient solver for the Poisson equation\n",
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{
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{
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{
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},
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"We begin by using {py:func}`create_rectangle\n",
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{
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},
{
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"The second argument to {py:class}`functionspace\n",
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{
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},
{
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"We now find the degrees of freedom that are associated with the boundary\n",
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{
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},
{
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"and use {py:func}`dirichletbc <dolfinx.fem.dirichletbc>` to define the\n",
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{
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},
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"Next, we express the variational problem using UFL."
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},
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"For the matrix-free solvers we also define a second linear form `M` as\n",
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{
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},
{
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"### Matrix-free conjugate gradient solver\n",
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{
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{
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},
{
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"This matrix-free solver is now used to compute the finite element solution.\n",
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{
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{
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"cells": [
{
"cell_type": "markdown",
"id": "2c7616fb",
"id": "b2c6452d",
"metadata": {},
"source": [
"# Mixed formulation for the Poisson equation"
]
},
{
"cell_type": "markdown",
"id": "b744eafd",
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"metadata": {},
"source": [
"This demo illustrates how to solve Poisson equation using a mixed\n",
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},
{
"cell_type": "markdown",
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"id": "4b3c0257",
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"```{admonition} Download sources\n",
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