Mimetic Covariant Discretization of Connections over Curvilinear Domains

Abstract

The present research aims at establishing a numerical technique that allows for simple discretization of curved domains. The method of implementation features use of covariant exterior derivatives that are used alongside structure preserving mixed mimetic spectral methods, that is primal and algebraic dual polynomials. A single element implementation is used to demonstrate the applicability of the method over two diffeomorphisms, a horizontal shear with non-linear skew and a modified polar coordinate transformation, for 0-forms and 1-forms. Finally, an extension of this framework towards continuum mechanics is discussed with a discussion over a co-vector valued stress and elasticity formulation.