Displaying similar documents to “Dual finite element analysis for an inequality of the 2nd order”

On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation

Michal Křížek, Pekka Neittaanmäki (1989)

Aplikace matematiky

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The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.

The density of solenoidal functions and the convergence of a dual finite element method

Ivan Hlaváček (1980)

Aplikace matematiky

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A proof is given of the following theorem: infinitely differentiable solenoidal vector - functions are dense in the space of functions, which are solenoidal in the distribution sense only. The theorem is utilized in proving the convergence of a dual finite element procedure for Dirichlet, Neumann and a mixed boundary value problem of a second order elliptic equation.

Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains

Michal Křížek, Pekka Neittaanmäki (1984)

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The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given. ...

Solvability of a first order system in three-dimensional non-smooth domains

Michal Křížek, Pekka Neittaanmäki (1985)

Aplikace matematiky

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A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain Ω ⊂ 𝐑 3 . On the boundary δ Ω , the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.