Displaying similar documents to “Green's theorem from the viewpoint of applications”

Identification of critical curves. II. Discretization and numerical realization

Jaroslav Haslinger, Václav Horák, Pekka Neittaanmäki, Kimmo Salmenjoki (1991)

Applications of Mathematics

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We consider the finite element approximation of the identification problem, where one wishes to identify a curve along which a given solution of the boundary value problem possesses some specific property. We prove the convergence of FE-approximation and give some results of numerical tests.

Examples from the calculus of variations. III. Legendre and Jacobi conditions

Jan Chrastina (2001)

Mathematica Bohemica

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We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding...

Semiregular finite elements in solving some nonlinear problems

Jana Zlámalová (2001)

Applications of Mathematics

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In this paper, under the maximum angle condition, the finite element method is analyzed for nonlinear elliptic variational problem formulated in [4]. In [4] the analysis was done under the minimum angle condition.

Examples from the calculus of variations. IV. Concluding review

Jan Chrastina (2001)

Mathematica Bohemica

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Variational integrals containing several functions of one independent variable subjected moreover to an underdetermined system of ordinary differential equations (the Lagrange problem) are investigated within a survey of examples. More systematical discussion of two crucial examples from Part I with help of the methods of Parts II and III is performed not excluding certain instructive subcases to manifest the significant role of generalized Poincaré-Cartan forms without undetermined...