Uniform in ε convergence of the standard Galerkin finite element method in L2-norm for the singularly-perturbed elliptic problems on a priori chosen meshes

Convection-diffusion problems are models for describing the transportation of matters in a diffusive medium. They are also a part of more general equations, such as the Navier-Stokes equations appearing in fluid flow problems. We consider the linear convection-diffusion problem of the special form and show that under the corresponding conditions...

akselson.pdf1.71 MB

Pseudo-orthogonal polynomials

The classical problem of the transformation of the orthogonality weights of polynomials by theory of the space Rn is discussed. The described system of polynomials - pseudo-orthogonal on the discrete set of n points - is a new result. The polynomials of this system, as the orthogonal ones, are...

kuznecov.pdf1.42 MB

Finite element trace theorems

The theorems on traces of functions from the Sobolev spaces play an important role in studying boundary value problems of mathematical physics. These theorems are commonly used for a priori estimates of the stability with respect to boundary conditions. The trace theorems play also very important role to construct and...

nepomnyashchih.pdf1.97 MB