In this paper we generalise results regarding the order of accuracy of finite difference operators on Summation-By-Parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary ste...

A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter ε, is examined. Due to the discontinuity an interior layer appears in the solution. A finite difference method is constructed for solving this problem, which generates ε-uniformly convergent numerical approximations to the solution. The method uses a piecewise u...

A new Fornberg-like method is presented for computing conformal maps from the interior of the unit disk with m−1 circular holes to the interior of a smooth closed curve with m−1 holes bounded by smooth curves. The method is a Newton-like method for computing the boundary correspondences and the conformal moduli (centers and radii of the circles). The inner linear systems are derived from condit...

For a stationary nonlinear Boltzmann equation in a slab with a particular truncation in the collision operator, the Milne problem for the boundary layer together with a weak type of hydrodynamic behaviour in the interior of the slab, are studied by non-perturbative methods in the small mean free path limit.

In this paper we clarify that the interior proximal method developed in [6] (vol. 27 of this journal) for solving variational inequalities with monotone operators converges under essentially weaker conditions concerning the functions describing the ”feasible” set as well as the operator of the variational inequality.

We consider propositional modal logic with two modal operators and [ 6 =]. In topological semantics is interpreted as an interior operator and [ 6=] as difference. We show that some important topological properties are expressible in this language. In addition, we present a few logics and proofs of f.m.p. and of completeness theorems.

We derive a weighted L-estimate of the Witten spinor in a complete Riemannian spin manifold (Mn, g) of non-negative scalar curvature which is asymptotically Schwarzschild. The interior geometry of M enters this estimate only via the lowest eigenvalue of the square of the Dirac operator on a conformal compactification of M .

We give an answer to an open problem regarding the full enlargeability of a maximal monotone operator S : X ⇒ X∗ by Sse, the smallest enlargement belonging to a certain class of enlargements associated to S. Moreover, we prove the weak∗ closedness of the set ShS (ε1, x)+ThT (ε2, x) under a weak generalized interior regularity condition.

Let u^ be a Ritz-Galerkin approximation, corresponding to the solution u of an elliptic boundary value problem, which is based on a uniform subdivision in the interior of the domain. In this paper we show that by "averaging" the values of Uu in the neighborhood of a point x we may (for a wide class of problems) construct an approximation to u(x) which is often a better approximation than UyAx) ...

Let H = −d/dx + V (x) be a Schrödinger operator on L2(0,∞) with spectral measure ρ, and suppose that the potential V is known on an initial interval [0, N ]. We show that this information yields strong restrictions on ρ(I) for intervals I ⊂ R. More precisely, we prove upper and lower bounds on ρ(I). The upper bound is finite for any I that is bounded above and the lower bound is positive if the...