The Recovery Of The Value And Derivatives At Nodes For Piecewise L~2 Projection And Interpolation

This paper studies the recovery of the value and derivatives at nodes for piecewiseL~2 projection and Lagrange interpolation. For the piecewise 2projection or Lagrange interpolation of a smooth function, we can choose appropriate symmetry sub-intervals within element patch at nodes and obtain a polynomial by 2projection. The value and derivatives of polynomial at nodes can be defined as recovered value and derivatives.The new recovery algorithm can get superconvergent recovery, and numerical examples verifies the theoretical result.