Study guide: Introduction to finite element methods

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Variable coefficient; variational formulation

Variational formulation.

Find $ (u-B)\in V $ such that $$ \int_{\Omega} \dfc(x)\frac{du}{dx}\frac{dv}{dx}dx = \int_{\Omega} f(x)vdx,\quad \forall v\in V $$

Compact notation: $$ \underbrace{(\dfc u',v')}_{a(u,v)} = \underbrace{(f,v)}_{L(v)}, \quad \forall v\in V $$