weak forms and FEM by Simon Shaw https://padlet.com/simon_shaw89/lang8kn59uup weak formulation and finite element approximation of elliptic PDE's en-us 2017-05-30 13:32:29 UTC 2025-10-02 12:55:48 UTC hello@padlet.com https://padlet-assets.s3.amazonaws.com/icons/Clouds.png This is a test simon_shaw89 https://padlet.com/simon_shaw89/lang8kn59uup/wish/174409952 x = y^2
Just highlight the LaTeX (or maybe use $$ ... $$) and click the \pi symbol
]]> 2017-05-30 13:35:43 UTC https://padlet.com/simon_shaw89/lang8kn59uup/wish/174409952 The Boundary Value Problem (BVP) simon_shaw89 https://padlet.com/simon_shaw89/lang8kn59uup/wish/174412566 -\nabla^2 u = f\ \text{in}\ \Omega

u = 0\ \text{on}\ \Gamma_D

\bold{n}\cdot\nabla u = g\ \text{on}\ \Gamma_N]]> 2017-05-30 13:45:05 UTC https://padlet.com/simon_shaw89/lang8kn59uup/wish/174412566 Integration by parts simon_shaw89 https://padlet.com/simon_shaw89/lang8kn59uup/wish/174413743 -\int_\Omega v\nabla^2 u\, d\Omega= \int_\Omega\nabla u\cdot\nabla v\, d\Omega -\int_{\partial\Omega} v\bold{n}\cdot\nabla u\, d\Gamma ]]> 2017-05-30 13:49:45 UTC https://padlet.com/simon_shaw89/lang8kn59uup/wish/174413743 Weak Formulation simon_shaw89 https://padlet.com/simon_shaw89/lang8kn59uup/wish/174414751 \text{Find}\ u\in V := \{v\in H^1(\Omega)\colon v=0\ \text{on}\ \Gamma_D\}\ \text{such that}

(\nabla u,\nabla v) = (f,v) + (g, v)_{\Gamma_N}\quad\forall v\in V]]> 2017-05-30 13:53:17 UTC https://padlet.com/simon_shaw89/lang8kn59uup/wish/174414751 Finite Element Method simon_shaw89 https://padlet.com/simon_shaw89/lang8kn59uup/wish/174416369 \text{Find}\ u_h\in V^h\subset V\ \text{such that}

(\nabla u_h,\nabla v) = (f,v) + (g, v)_{\Gamma_N}\quad\forall v\in V^h]]> 2017-05-30 13:59:08 UTC https://padlet.com/simon_shaw89/lang8kn59uup/wish/174416369 How does the FEM work? simon_shaw89 https://padlet.com/simon_shaw89/lang8kn59uup/wish/174459640 Let's look at the main steps...]]> 2017-05-30 16:50:25 UTC https://padlet.com/simon_shaw89/lang8kn59uup/wish/174459640 Linear System simon_shaw89 https://padlet.com/simon_shaw89/lang8kn59uup/wish/346045600 $$x\in\mathbb{R}$$ does this work in safari?]]> 2019-03-28 09:54:22 UTC https://padlet.com/simon_shaw89/lang8kn59uup/wish/346045600