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Čermák, Libor

The finite element solution of second order elliptic problems with the Newton boundary condition. (English) Zbl 0542.65063

Apl. Mat. 28, 430-456 (1983).
The convergence in both the \(H^ 1\) and \(L_ 2\) norms for a second order elliptic problem in n-dimensional Euclidean space (\(n\geq 2)\) with Newton boundary condition is analysed. Following P. G. Ciarlet and P. A. Raviart [Math. Found. finite Elem. Method Appl. part. differ. Equations, Sympos. Univ. Maryland, Baltimore 1972, 409-474 (1972; Zbl 0262.65070)] the author introduces the numerical isoparametric integration on both ”volume” and surface elements and analyses the obtained fully discrete problem. An estimate for the discretization error in \(H^ 1\) and \(L_ 2\) norms is given.
Reviewer: P.Chocholatý

Cited in 4 Documents

MSC:

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

Keywords:

convergence; finite element; Newton boundary condition; simplicial isoparametric elements; error estimates

Citations:

Zbl 0262.65070
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\textit{L. Čermák}, Apl. Mat. 28, 430--456 (1983; Zbl 0542.65063)
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References:

[1] P. G. Ciarlet: The Finite Element Method for Elliptic Problems. North-Holland. Amsterdam. 1978. · Zbl 0383.65058
[2] P. G. Ciarlet P. A. Raviart: The combined effect of curved boundaries and numerical integration in isoparametric finite element methods. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz Editor). Academic Press. New York and London. 1972. · Zbl 0262.65070
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