Mesh-Centered Finite Differences from Nodal Finite Elements

After it is shown that the classical ve points mesh-centered nite diierence scheme can be derived from a low order nodal nite element scheme by using nonstandard quadrature formulae, higher order block mesh-centered nite diierence schemes for second-order elliptic problems are derived from higher order nodal nite elements with nonstandard quadrature formulae as before, combined to a procedure known as \transverse integration". Numerical experiments with uniform and nonuniform meshes and diierent types of boundary conditions connrm the theoretical predictions, in discrete as well as continuous norms. Dii erences Finies Centr ees a partir d'El ements Finis Nodaux R esum e : Apr es avoir montr e que le sch ema en dii erences nies centr e clas-sique a cinq points peut ^ etre obtenu a partir d'un el ement ni nodal de bas ordre en utilisant des formules de quadrature num eriques non standard, on d eveloppe des sch emas a cinq blocs d'ordre plus elev e avec des quadratures num eriques non standard comme plus haut, combin ees avec une proc edure connue sous le nom d'int egration transversale. Des exp eriences num eriques avec des mailles uniformes ou pas et dii erents types de conditions a la fron-ti ere, connrment les pr edictions th eoriques en normes continues et discr etes.