论文信息 - On the numerical analysis of the Von Karman equations: Mixed finite element approximation and continuation techniques

On the numerical analysis of the Von Karman equations: Mixed finite element approximation and continuation techniques

SummaryThe purpose of this paper is to study the approximation of the Von Karman equations by the mixed finite element scheme of Miyoshi and to follow the solutions arcs at a neighbourhood of the first eigenvalue of the linearized problem. This last problem is solved by a continuation method.

L. Reinhart | Laure Reinhart

[1] Reinhard Scholz. A mixed method for 4th order problems using linear finite elements , 1978 .

[2] Melvyn S. Berger,et al. On von kármán's equations and the buckling of a thin elastic plate, I the clamped plate , 1967 .

[3] Tetsuhiko Miyoshi,et al. A mixed finite element method for the solution of the von Kármán equations , 1976 .

[4] J. Nitsche,et al. $L_\infty $-Convergence of Finite Element Approximation , 1975 .

[5] T. Kármán. Festigkeitsprobleme im Maschinenbau , 1907 .

[6] S. G. Mikhlin,et al. The problem of the minimum of a quadratic functional , 1965 .

[7] J. Nitsche,et al. L∞-convergence of finite element approximations , 1977 .

[8] H. Keller,et al. Buckled states of circular plates , 1962 .

[9] F. Brezzi,et al. Finite element approximations of the von Kármán equations , 1978 .

[10] P. G. Ciarlet,et al. Les équations de Von Kármán , 1980 .

[11] Philippe G. Ciarlet,et al. A justification of the von Kármán equations , 1980 .

[12] Rolf Rannacher,et al. On nonconforming an mixed finite element methods for plate bending problems. The linear case , 1979 .

[13] V. A. Kondrat'ev,et al. Boundary problems for elliptic equations in domains with conical or angular points , 1967 .