Wave equation. P1 or P2 and no need for remeshing here.
\begin{array}{rcl} \partial_{tt}u-\nu \,\partial_{xx}u& =&0 \quad\mbox{on } (0,1),\\ u(0,t)=0,\;u(1,t) & =&0,\\ u(x,0)&=&u_0(x) \end{array}
Different snapshots of the solution. We use P2 finite elements and a row of triangles sitting on the 1d interval to use the freefem tools
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download example : WaveEquation-1d.edp