This paper presents analysis of a weighted-norm least squares finite element method for elliptic problems with boundary singularities. We use H(div) conforming Raviart–Thomas elements and continuous piecewise polynomial elements. With only a rough estimate of the power of the singularity, we employ a simple, locally weighted L2 norm to eliminate the pollution effect and recover better rates of ...

We prove an algebraic formula for the Euler characteristic of the Milnor fibres of functions with critical locus a smooth curve on a space which is a weighted homogeneous complete intersection with isolated singularity.

Given a three-dimensional complex algebraic variety with isolated singular point and a sufficiently fine complete resolution of the singularity, we can make a careful choice of hyperplane that allows us to construct an exact sequence of weighted Nash complexes.

Mathematical models of fracture physics and mechanics are boundary value problems for differential equations systems with a singularity. There two classes singularity: coordinated uncoordinated degeneracy the input data, depending on behavior coefficients equation. Finite element methods first order convergence rate O(h) have been created to find an approximate solution these problems. We const...

The weighted finite element method makes it possible to find an approximate solution of a boundary value problem with corner singularity without loss accuracy. construction this numerical is based on the introduction concept Rν-generalized for singularity. In paper, special sets corresponding operators from definition Stokes in nonsymmetric variational formulation are introduced. properties and...

This paper is the first in a series devoted to the approximation theory of the p-version of the finite element method in three dimensions. In this paper, we introduce the Jacobi-weighted Besov and Sobolev spaces in the three-dimensional setting and analyze the approximability of functions in the framework of these spaces. In particular, the Jacobi-weighted Besov and Sobolev spaces with three di...

In this paper, we consider localized integral operators whose kernels have mild singularity near the diagonal and certain Hölder regularity and decay off the diagonal. Our model example is the Bessel potential operator Jγ , γ > 0. We show that if such a localized integral operator has stability on a weighted function space Lw for some p ∈ [1,∞) and Muckenhoupt Ap-weight w, then it has stability...

We deene a series of non-negative integer valued invariants (1) of an analytic n-dimensional isolated complete intersection singularity (the generalized Tjurina numbers). The Tjurina number is equal to (1). We show that all these numbers are bounded by the Milnor number by establishing explicit formulas for the diierences ? (p) involving the mixed Hodge numbers of the cohomology of the link. Th...