Asymptotic Expansion for the Discretization Error in Linear Elliptic Boundary Value Problems on General Regions.
Asymptotic Expansions and L...-Error Estimates for Mixed Finite Element Methods for Second Order Elliptic Problems.
Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
We consider solutions to the time-harmonic Maxwell's Equations of a TE (transverse electric) nature. For such solutions we provide a rigorous derivation of the leading order boundary perturbations resulting from the presence of a finite number of interior inhomogeneities of small diameter. We expect that these formulas will form the basis for very effective computational identification algorithms, aimed at determining information about the inhomogeneities from electromagnetic boundary measurements. ...
Asymptotic models for scattering from unbounded media with high conductivity
We analyze the accuracy and well-posedness of generalized impedance boundary value problems in the framework of scattering problems from unbounded highly absorbing media. We restrict ourselves in this first work to the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficulties in the analysis for the generalized impedance boundary conditions, since classical compactness arguments are no...
Asymptotic profile of a radially symmetric solution with transition layers for an unbalanced bistable equation.
Asymptotic stability of a 9-point multigrid algorithm for convection-diffusion equations.
Asymptotics and estimates of the convergence rate in a three-dimensional boundary value problem with rapidly alternating boundary conditions.
Asymptotics for quasilinear elliptic non-positone problems
In the recent years, many results have been established on positive solutions for boundary value problems of the form in Ω, u(x)=0 on ∂Ω, where λ > 0, Ω is a bounded smooth domain and f(s) ≥ 0 for s ≥ 0. In this paper, a priori estimates of positive radial solutions are presented when N > p > 1, Ω is an N-ball or an annulus and f ∈ C¹(0,∞) ∪ C⁰([0,∞)) with f(0) < 0 (non-positone).
Asymptotics of solutions to some boundary value problems of elasticity for bodies with cuspidal edges.
Asymptotics of the first boundary problem for elliptic equations in a domain with thin covering.
Autovalori di un problema ellittico dipendente da un parametro in modo non lineare
Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements
An averaging method for the second-order approximation of the values of the gradient of an arbitrary smooth function u = u(x 1, x 2) at the vertices of a regular triangulation T h composed both of rectangles and triangles is presented. The method assumes that only the interpolant Πh[u] of u in the finite element space of the linear triangular and bilinear rectangular finite elements from T h is known. A complete analysis of this method is an extension of the complete analysis concerning the finite...
Aппроксимация обобщенных решений с помощью конечных разностей
Behavior of plane relaxation methods as multigrid smoothers.
Bernstein approximations of Dirichlet problems for elliptic operators on the plane.
Besov Regularity for Second Order Elliptic Boundary Value Problems with Variable Coefficients.
Best possible estimates of solutions to the transmission problem for the Laplace operator with N different media in a conical domain
We investigate the behavior of weak solutions to the transmission problem for the Laplace operator with N different media in a neighborhood of a boundary conical point. We establish a precise exponent of the decreasing rate of the solution.
Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent.
Borderline sharp estimates for solutions to Neumann problems.
Boundaries of graphs of harmonic functions.