Convergence analysis of some numerical quadrature schemes for a nonconforming finite element method. (English) Zbl 1205.65299
The authors discuss a nonconforming quadrilateral finite element method for a general second order elliptic problem. Some optimal numerical quadrature formulas are presented and analyzed, and the novelty is that it includes a formula with only three sampling points. With this numerical quadrature method, optimal error estimates for general second order elliptic problems are derived. Lastly, some numerical results are provided to verify the theoretical analysis.
Reviewer: I. N. Katz (St. Louis)
MSC:
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 65D32 | Numerical quadrature and cubature formulas |
| 41A55 | Approximate quadratures |
