Discrete Equivalence of Adjoint Neumann-Dirichlet div-grad and grad-div Equations in Curvilinear 3D Domains

摘要

By constructing and using primal polynomial spaces and their algebraic dual representations both in the domain and on the boundary, we successfully preserve the equivalence of the div-grad Neumann problem and the grad-div Dirichlet problem at the discrete level in 3-dimensional curvilinear domains. This suggests the further usage of these spaces to structure-preserving methods and hybrid methods.