Nonlinear positive interpolation operators for analysis with multilevel grids

Abstract

We introduce some nonlinear positive and negative interpolation operators. The interpolation need to preserve positivity or negativity of a function. In addition, the interpolation must be pointwise below or above the function. Some of the operators also have the pointwise monotone property over refined meshes. It is also desirable that the interpolation have the needed approximation and stability estimates. Those operators could be used in the convergence analysis for domain decomposition and multigrid methods for obstacle problems.