A Mimetic Discretization of Elliptic Obstacle Problems
Wednesday 2nd June 2010
Antonietti, Paola F. ; Beirao da Veiga, Lourenco; Verani, Marco
We develop a Finite Element method (FEM) which can adopt very general meshes with polygonal elements for the numerical approximation of elliptic obstacle problems. This kind 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. Keywords: Mimetic Finite Difference Methods, obstacle problem. 2000 Mathematics Subject Classication. Primary 65N30; Secondary 35R35.