Quasi-Optimal Meshes for Gradient Nonconforming Approximations

We consider anisotropic adaptive methods based on a metric related to the Hessian of the solution. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain Omega of R-d,d >= 2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative to such a nonconforming discretization and give numerical asymptotic behavior of the error reduction produced by the generated mesh. Numerical experiments are performed to generate mesh minimizing interpolation error gradient of benchmark functions, and nonconforming approximation of solution of a PDE as convection diffusion equation selected for this note.