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      <title>ModularEIT Wiki</title>
      <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki</link>
      <description>Last 10 notes on ModularEIT Wiki</description>
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    <title>Conformal Invariance of the Conductivity Equation</title>
    <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/02-The-Forward-Problem/Conformal-Invariance-of-the-Conductivity-Equation</link>
    <guid>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/02-The-Forward-Problem/Conformal-Invariance-of-the-Conductivity-Equation</guid>
    <description><![CDATA[ In two dimensions the Conductivity Equation is invariant under conformal maps. ]]></description>
    <pubDate>Thu, 01 Oct 2026 12:58:28 GMT</pubDate>
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    <title>Boundary Mass and Stiffness Matrices</title>
    <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Boundary-Mass-and-Stiffness-Matrices</link>
    <guid>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Boundary-Mass-and-Stiffness-Matrices</guid>
    <description><![CDATA[ Boundary data (voltages f, currents g) are functions on \partial\Omega. ]]></description>
    <pubDate>Thu, 01 Oct 2026 12:58:28 GMT</pubDate>
  </item><item>
    <title>Galerkin Method</title>
    <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Galerkin-Method</link>
    <guid>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Galerkin-Method</guid>
    <description><![CDATA[ A Galerkin method approximates a variational problem \text{find } u\in V:\quad a(u,v) = \ell(v)\quad\forall v\in V by replacing the infinite-dimensional space V with a finite-dimensional subspace V_h = \operatorname{span}\{\varphi_1,\dots,\varphi_n\}. ]]></description>
    <pubDate>Thu, 01 Oct 2026 12:58:28 GMT</pubDate>
  </item><item>
    <title>L2 Projection</title>
    <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/L2-Projection</link>
    <guid>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/L2-Projection</guid>
    <description><![CDATA[ The L^2 projection of a function w onto a finite element space V_h=\operatorname{span}\{\varphi_i\} is the best approximation in L^2(\Omega): P_hw = \arg\min_{v_h\in V_h}\|w-v_h\|_{L^2} \quad\Longleftrightarrow\quad M\,\mathbf z = \mathbf b,\qquad b_i = \int_\Omega w\,\varphi_i\,\mathrm dx , with th... ]]></description>
    <pubDate>Thu, 01 Oct 2026 12:58:28 GMT</pubDate>
  </item><item>
    <title>Lagrange Finite Elements</title>
    <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Lagrange-Finite-Elements</link>
    <guid>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Lagrange-Finite-Elements</guid>
    <description><![CDATA[ Lagrange elements use piecewise polynomial basis functions defined by their values at nodes. ]]></description>
    <pubDate>Thu, 01 Oct 2026 12:58:28 GMT</pubDate>
  </item><item>
    <title>Mass Matrix</title>
    <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Mass-Matrix</link>
    <guid>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Mass-Matrix</guid>
    <description><![CDATA[ The mass matrix is the Gram matrix of the basis in L^2(\Omega): M_{ij} = \int_\Omega\varphi_i\,\varphi_j\,\mathrm dx . ]]></description>
    <pubDate>Thu, 01 Oct 2026 12:58:28 GMT</pubDate>
  </item><item>
    <title>Pixel Images and Finite Element Functions</title>
    <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Pixel-Images-and-Finite-Element-Functions</link>
    <guid>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Pixel-Images-and-Finite-Element-Functions</guid>
    <description><![CDATA[ Learned priors, image denoisers and plots work with pixel images, while the forward problem works with finite element coefficients. ]]></description>
    <pubDate>Thu, 01 Oct 2026 12:58:28 GMT</pubDate>
  </item><item>
    <title>Stiffness Matrix</title>
    <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Stiffness-Matrix</link>
    <guid>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/04-Finite-Elements/Stiffness-Matrix</guid>
    <description><![CDATA[ The (unweighted) stiffness matrix discretises the Laplacian: K_{ij} = \int_\Omega\nabla\varphi_i\cdot\nabla\varphi_j\,\mathrm dx,\qquad \mathbf z^\top K\mathbf z = \|\nabla z_h\|^2_{L^2(\Omega)} . ]]></description>
    <pubDate>Thu, 01 Oct 2026 12:58:28 GMT</pubDate>
  </item><item>
    <title>Fast Solvers on Disk Domains</title>
    <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/05-Linear-Solvers/Fast-Solvers-on-Disk-Domains</link>
    <guid>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/05-Linear-Solvers/Fast-Solvers-on-Disk-Domains</guid>
    <description><![CDATA[ On a disk, the constant-coefficient Neumann problem separates in polar coordinates: Fourier modes in the angle, and one ordinary differential equation along the radius per mode. ]]></description>
    <pubDate>Thu, 01 Oct 2026 12:58:28 GMT</pubDate>
  </item><item>
    <title>A Posteriori Error Estimation and Adaptive Meshing</title>
    <link>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/06-Meshes-and-Geometry/A-Posteriori-Error-Estimation-and-Adaptive-Meshing</link>
    <guid>https://danielboigk.github.io/ModularEIT.jl/dev/wiki/06-Meshes-and-Geometry/A-Posteriori-Error-Estimation-and-Adaptive-Meshing</guid>
    <description><![CDATA[ A finite element solution u_h satisfies the discrete equations exactly. ]]></description>
    <pubDate>Thu, 01 Oct 2026 12:58:28 GMT</pubDate>
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