Second order elliptic systems with boundary conditions of Dirichlet, Neumann’s or Newton’s type are solved by means of linear finite elements on regular uniform triangulations. Error estimates of the optimal order are proved for the averaged gradient on any fixed interior subdomain, provided the problem under consideration is regular in a certain sense.
We construct a testing function space, which is equipped with the topology that is generated by Lν,p - multinorm of the differential operatorAx = x2 - x d/dx [x d/dx],and its k-th iterates Akx, where k = 0, 1, ... , and A0xφ = φ. Comparing with other testing-function spaces, we introduce in its dual the Kontorovich-Lebedev transformation for distributions with respect to a complex index. The existence, uniqueness, imbedding and inversion properties are investigated. As an application we find a solution...
We consider the local projection finite element method for the discretization of a scalar convection-diffusion equation with a divergence-free convection field. We introduce a new fluctuation operator which is defined using an orthogonal projection with respect to a weighted inner product. We prove that the bilinear form corresponding to the discrete problem satisfies an inf-sup condition with respect to the SUPG norm and derive an error estimate for the discrete solution.
In this paper we derive results concerning the angular distrubition of the eigenvalues and the completeness of the principal vectors in certain function spaces for an oblique derivative problem involving an indefinite weight function for a second order elliptic operator defined in a bounded region.
We prove that penalization of constraints occuring in the linear elliptic Neumann problem yields directly the exact solution for an arbitrary set of penalty parameters. In this case there is a continuum of Lagrange's multipliers. The proposed penalty method is applied to calculate the magnetic field in the window of a transformer.
We present some results concerning the problem , in , , where , , and is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.
Discretization of second order elliptic partial differential equations by discontinuous Galerkin method often results in numerical schemes with penalties. In this paper we analyze these penalized schemes in the context of quite general triangular meshes satisfying only a semiregularity assumption. A new (modified) penalty term is presented and theoretical properties are proven together with illustrative numerical results.
We investigate the solvability of a singular equation of Caffarelli-Kohn-Nirenberg type having a critical-like nonlinearity with a sign-changing weight function. We shall examine how the properties of the Nehari manifold and the fibering maps affect the question of existence of positive solutions.
We characterize some -limits using two-scale techniques and investigate a method to detect deviations from the arithmetic mean in the obtained -limit provided no periodicity assumptions are involved. We also prove some results on the properties of generalized two-scale convergence.
The paper deals with the problem of finding a curve, going through the interior of the domain , accross which the flux , where is the solution of a mixed elliptic boundary value problem solved in , attains its maximum.
The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an -dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an (-dimensional) rectangular grid in the directions of the individual...