Adaptivity Based on the Constitutive Error for the Maxwell's Eigenvalue Problem on Polyhedral Meshes

This paper first introduces a simplified construction of the constitutive matrices for general polyhedral meshes. These constitutive matrices are geometrically defined by means of simple closed-form expressions involving the geometric elements of the primal and dual meshes. Then, we solve for the first time the Maxwell's eigenvalue problem on general polyhedral meshes. In particular, we analyze the convergence of the eigenvalues when the mesh is adaptively refined by using the subgridding technique together with the constitutive inconsistency as error indicator.