A mimetic discretization of elliptic obstacle problems

We develop a Finite Element Method (FEM) which can adopt very general meshes with polygonal elements for the numerical approximation of elliptic obstacle problems. These kinds of methods are also known as mimetic discretization schemes, which stem from the Mimetic Finite Difference (MFD) method. The first-order convergence estimate in a suitable (mesh-dependent) energy norm is established. Numerical experiments confirming the theoretical results are also presented.