*(English)*Zbl 1087.65103

The paper deals with the accuracy of a nonconforming finite element methods for the well-known equation ${{\Delta}}^{2}u=f$ with the homogeneous Dirichlet conditions on the boundary of $\overline{{\Omega}}$ – a union of several rectangles.

On nonquasiuniform rectangular grids, the so called ACM’s nonconforming finite elements are considered. The main aim is to study the convergence under the usual assumption that $u\in {H}^{4}\left({\Omega}\right)$ but without such widely used restriction as a quasiuniform structure of the grid. The authors give an estimate of the type $O\left({h}_{max}^{2}\right)$ in a grid norm. They also present numerical examples for the grids of type $128\times 128$ and $64\times 384$.

In places the presentation is rather strange – for example, the authors call the equation “biharmonic” and write that “the domain is the union of rectangles”.

##### MSC:

65N15 | Error bounds (BVP of PDE) |

65N30 | Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) |

65N12 | Stability and convergence of numerical methods (BVP of PDE) |

35J40 | Higher order elliptic equations, boundary value problems |