Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus

Abstract We present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given simplicial mesh, we first refine the mesh into smaller simplices which can be used define forms. Cochains this refined then interpolated using Hence, when is with calculus, solution expressed as form. algorithms for three required steps: refining solving coefficients of interpolant, and evaluating interpolant at given point. With our algorithms, one wishes use parameter so that same code covers all orders, significant improvement previous implementations. Our are applicable degrees freedom integrals over — is, cochain mesh. They also simply approximate differential finite-dimensional spaces. Numerical examples validate generality algorithms.