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On the circumradius condition for piecewise linear triangular elements. (English) Zbl 1328.65052

Summary: We discuss the error analysis of linear interpolation on triangular elements. We claim that the circumradius condition is more essential than the well-known maximum angle condition for convergence of the finite element method, especially for the linear Lagrange finite element. Numerical experiments show that this condition is the best possible. We also point out that the circumradius condition is closely related to the definition of surface area.

MSC:

65D05 Numerical interpolation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
26B15 Integration of real functions of several variables: length, area, volume
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