The origins of the finite element method can be traced back to the 1950s when engineers started to solve numerically structural mechanics problems in aeronautics. Since then, the field of applications has widened steadily and nowadays encompasses nonlinear solid mechanics, fluid/structure interactions, flows in industrial or geophysical settings, multicomponent reactive turbulent flows, mass transfer in porous media, viscoelastic flows in medical sciences, electromagnetism, wave scattering problems, and option pricing (to cite a few examples). Numerous commercial and academic codes based on...

Ces notes de cours (Ecole Nationale des Ponts et Chaussees, DEA de Mecanique de Paris VI) presentent la methode des elements finis dans un cadre mathematique rigoureux. En accordant une place fondamentale aux conditions inf-sup, elles s'affranchissent du cadre reducteur Lax-Milgram/Galerkin standard. Elles couvrent un spectre d'applications relativement large et apportent de nombreuses precisions sur la mise en oeuvre numerique. Trois plans de lecture sont proposes: le premier concu pour un lecteur interesse par les aspects mathematiques, le deuxieme s' adressant aux ingenieurs et le...

The origins of the finite element method can be traced back to the 1950s when engineers started to solve numerically structural mechanics problems in aeronautics. Since then, the field of applications has widened steadily and nowadays encompasses nonlinear solid mechanics, fluid/structure interactions, flows in industrial or geophysical settings, multicomponent reactive turbulent flows, mass transfer in porous media, viscoelastic flows in medical sciences, electromagnetism, wave scattering problems, and option pricing (to cite a few examples). Numerous commercial and academic codes based on...