On the Best Constant in the Error Bound for theH10-Projection into Piecewise Polynomial Spaces Original Research Article

Explicita priorierror bounds for the approximation by theH10-projection into piecewise polynomial spaces are given. In particular, for the quadratic approximation, the optimal constant is derived, and a nearly optimal value for the cubic is obtained. These constants play an important role in the numerical verification method of finite element solutions for nonlinear elliptic equations.