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Intro Suppose we have the following static linear equations (e.g. of an elastostatic problem): $$\mathbf{K}\boldsymbol{u}=\boldsymbol{f}$$ We want a multipoint constraint of the type $$\boldsymbol{\...

I searched in many books regarding FEM how to solve semilinear elliptic equation, but I did not find too many things. They mostly treat linear and simple problems. For example in P.Ciarlet-The finite ...

Most FEM texts or tutorials apply FEMs on diffusion equations where the 2nd spatial derivative is integrated by parts during weak formulation. For convection diffusion equations, there is a first ...

According to this Wikipedia article: Spectral methods can be computationally less expensive and easier to implement than finite element methods; they shine best when high accuracy is sought in simple ...

Background: Consider the one-dimensional second-order elliptic PDE, $$ \left\{\!\! \begin{aligned} & -(a(x)u'(x))'+b(x)u(x)=f(x)\qquad x\in[0,1]\\ & u(0)=u(1)=0 \end{aligned} \...