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On the anisotropic accuracy analysis of ACM’s nonconforming finite element. (English) Zbl 1087.65103

The paper deals with the accuracy of a nonconforming finite element methods for the well-known equation Δ 2 u=f with the homogeneous Dirichlet conditions on the boundary of Ω ¯ – 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 uH 4 (Ω) but without such widely used restriction as a quasiuniform structure of the grid. The authors give an estimate of the type O(h max 2 ) in a grid norm. They also present numerical examples for the grids of type 128×128 and 64×384.

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:
65N15Error bounds (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
35J40Higher order elliptic equations, boundary value problems