0000000001333677
AUTHOR
Křížek, Michal
Solvability of a first order system in three-dimensional non-smooth domains
summary:A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain $\Omega\subset \bold R^3$. On the boundary $\delta\Omega$, the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.
On the validity of Friedrichs’ inequalities
A standard proof of Friedrich's second inequality is based on contradiction argumentation. In this paper a direct proof is presented. Moreover, necessary and sufficient conditions for the validity of Friedrichs' first and second inequality are given for plane domains. peerReviewed
On time-harmonic Maxwell equations with nonhomogeneous conductivities : Solvability and FE-approximation
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 probJem 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. peerReviewed
Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains
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. peerReviewed