Mimetic framework on curvilinear quadrilaterals of arbitrary order

• DOI: 10.48550/arxiv.1111.4304
• Publication Date: 2011-01-01
• Authors: Jasper Kreeft; Artur Palha; Marc Gerritsma
• Keywords: Quadrilateral; Realization (probability)

In this paper higher order mimetic discretizations are introduced which firmly rooted in the geometry variables defined. The shows how basic constructs differential have a discrete counterpart algebraic topology. Generic maps switch between continuous forms and cochains will be discussed finally realization of these ideas terms spectral elements is presented, based on projections for operations at finite dimensional level commute with level. two types orientation (inner- outer-orientation) level, preservation demonstrated new operators. one-to-one correspondence formulation topological setting, provides characterization oriented boundary domain. Hodge decomposition continuous, presented. It appears to main ingredient structure framework.