High-order polynomial reconstruction

Add polynomial reconstruction of arbitrary degree (as long as exact quadrature formula are available)

• 1d, 2d and 3d are supported
• use a generalized Horner like formula in any dimension (optimal evaluation)
• reconstruction can be performed in parallel (number of ghost layers may have to be adjust with the --number-of-ghost-layers running option
• symmetry boundary conditions are taken into account (on demand)
• one is encourage to reconstruct multiple variables at once: it reduces considerably the cost

Three methods are available to evaluate the integration of the polynomial basis in the stencil

• cell_center available for degree 1 reconstruction only. The most efficient,
• element use element base quadrature formulas. Restricted to elements for which a conform transformation is defined
• boundary use face based quadrature. Works for any polygonal cell and for any polytopal cell with triangle or quandragle faces (more expensive for low degrees).

Remains a bunch of developments:

• propose new kind of stencils
  • stencils are by now too large (try to build "optimal" ones?
  • allow restriction to zones of stencils
• define basic limitation strategies
• give access to reconstruction options in pgs scripts.