Mimetic finite difference operators and higher order quadratures

Abstract Mimetic finite difference operators $$\textbf{D}$$ D , $$\textbf{G}$$ G are discrete analogs of the continuous divergence (div) and gradient (grad) operators. In sense, these satisfy same properties as those their continuum counterparts. particular, they a extended Gauss’ theorem. This paper investigates higher-order quadratures associated with fourth- sixth- order mimetic operators, show that indeed numerical addition, extensions to curvilinear coordinates treated. Examples in one two dimensions illustrate results presented confirm validity theoretical findings.