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lines changed Original file line number Diff line number Diff line change @@ -136,8 +136,8 @@ <h3>Weak formulation<a class="headerlink" href="#weak-formulation" title="Link t
136136\forall \ K \in \mathcal{T} \right\}
137137\]</ div >
138138< p > and considering the boundary conditions</ p >
139- < div class ="amsmath math notranslate nohighlight " id ="equation-e06759a1-4b09-4b2e-ab7b-0ca1bd5cb393 ">
140- < span class ="eqno "> (1)< a class ="headerlink " href ="#equation-e06759a1-4b09-4b2e-ab7b-0ca1bd5cb393 " title ="Permalink to this equation "> </ a > </ span > \[\begin{align}
139+ < div class ="amsmath math notranslate nohighlight " id ="equation-b98e6532-a7ed-4caa-89f4-f27fc556c4db ">
140+ < span class ="eqno "> (1)< a class ="headerlink " href ="#equation-b98e6532-a7ed-4caa-89f4-f27fc556c4db " title ="Permalink to this equation "> </ a > </ span > \[\begin{align}
141141u &= 0 \quad {\rm on} \ \partial\Omega, \\
142142\nabla^{2} u &= 0 \quad {\rm on} \ \partial\Omega,
143143\end{align}\]</ div >
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88 " # Matrix-free conjugate gradient solver for the Poisson equation\n " ,
7373 {
7474 "cell_type" : " code" ,
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108108 "metadata" : {},
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110110 " We begin by using {py:func}`create_rectangle\n " ,
117117 {
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144- "id" : " 55d0c6ed " ,
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145145 "metadata" : {},
146146 "source" : [
147147 " The second argument to {py:class}`functionspace\n " ,
160160 {
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177177 " We now find the degrees of freedom that are associated with the boundary\n " ,
182182 {
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197197 " and use {py:func}`dirichletbc <dolfinx.fem.dirichletbc>` to define the\n " ,
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205205 "cell_type" : " code" ,
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221221 " Next, we express the variational problem using UFL."
224224 {
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245245 " For the matrix-free solvers we also define a second linear form `M` as\n " ,
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272272 " ### Matrix-free conjugate gradient solver\n " ,
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410410 " This matrix-free solver is now used to compute the finite element\n " ,
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