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On interpolation error on degenerating prismatic elements. (English) Zbl 06945731
Summary: We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P. G. Ciarlet [The finite element method for elliptic problems. Amsterdam: North-Holland Publishing Company (1978; Zbl 0383.65058)], but the interpolation error remains of the order \(O(h)\) in the \(H^1\)-norm for sufficiently smooth functions.

MSC:
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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