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The construction of finite element approximations in $\mathbf{H}(\mbox{div},{\Omega})$ usually requires the Piola transformation to map vector polynomialsfrom a master element to vector fields in the elements of a partition of theregion {\Omega}. It is known that degradation may occur in convergence order ifnon affine geometric mappings are used. On this point, we revisit a generalprocedure for the improvement of two-dimensional flux approximations discussedin a recent paper of this journal (Comput. Math. Appl. 74 (2017) 3283-3295).The starting point is an approximation scheme, which is known to provide$L^2$-errors with accuracy of order $k+1$ for sufficiently smooth fluxfunctions, and of order $r+1$ for flux divergence. An example is $RT_{k}$spaces on quadrilateral meshes, where $r = k$ or $k-1$ if linear or bilineargeometric isomorphisms are applied. Furthermore, the original space is requiredto be expressed by a factorization in terms of edge and internal shape fluxfunctions. The goal is to define a hierarchy of enriched flux approximations toreach arbitrary higher orders of divergence accuracy $r+n+1$ as desired, forany $n \geq 1$. The enriched versions are defined by adding higher degreeinternal shape functions of the original family of spaces at level $k+n$, whilekeeping the original border fluxes at level $k$. The case $n=1$ has beendiscussed in the mentioned publication for two particular examples. Generalstronger enrichment $n>1$ shall be analyzed and applied to Darcy's flowsimulations, the global condensed systems to be solved having same dimensionand structure of the original scheme.

A remark concerning divergence accuracy order for H(div)-conforming finite element flux approximations