Second order convergence of the interpolation based on \(Q_1^c\)-element. (English) Zbl 1399.65026
Summary: In this paper, the second order convergence of the interpolation based on \(Q_1^c\)-element is derived in the case of \(d=1, 2\) and 3. Using the integral average on each element, the new basis function of tensor product type is built up and we can easily extend it to the higher dimensional case. Finally, some numerical tests are made to show the analytical results of the interpolation errors.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35Q30 | Navier-Stokes equations |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65D05 | Numerical interpolation |
