Extensions from into (where ) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary of . The corresponding extension operator is linear and bounded.
In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell’s equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.
In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell's equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.
Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving norms obtained by Nečas and on the general framework of Γ-convergence theory.