We analyse the error of interpolation of functions from the space H(a, c) in the nodes a < b < c of a regular quadratic Lagrange finite element in 1D by interpolants from the local function space of this finite element. We show that the order of the error depends on the way in which the mutual positions of nodes a, b, c change as the length of interval [a, c] approaches zero.

Oxley has conjectured that for k ≥ 4, if a matroidM has a k-element set that is the intersection of a circuit and a cocircuit, thenM has a (k− 2)-element set that is the intersection of a circuit and a cocircuit. In this paper we prove a stronger version of this conjecture for regular matroids. We also show that the stronger result does not hold for binary matroids.

Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and...

this paper is the second of a two part series. in this part, we prove, using the description of simples obtained in part i, that the variety $mathbf{rdqdstsh_1}$ of regular dually quasi-de morgan stone semi-heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{rdqdstsh_1}$-chains and the variety of dually quasi-de morgan boolean semi-heyting algebras--...

In this paper we describe the theory and code implementation of a tool to obtain the time-dependent pressure distribution on a marine structure using the results from a boundary element method code (BEM). Here, we present a case study of a floating wave energy converter (WEC) in regular waves. The results are verified by comparison with open-source codes and then used to run a structural simula...

This letter shows that for every finite element triangulation in R, there exists a coloring where each triangle has exactly one red and two black edges. This result is shown using Petersen’s Theorem which states that all bridgeless 3-regular graphs have a perfect matching. The existence of such a coloring has useful applications when the finite element method is applied to problems with solutio...

Interpolation operators map a function u to an element Iu of a finite element space. Unlike more general approximation operators, interpolants are defined locally. Estimates of the interpolation error, i.e., the difference u− Iu, are of utmost importance in numerical analysis. These estimates depend on the size of the finite elements, the polynomial degree employed, and the regularity of u. In ...

The one-lie Rényi-Ulam liar game is a 2-player perfect information zero sum game, lasting q rounds, on the set [n] := {1, . . . , n}. In each round Paul chooses a subset A ⊆ [n] and Carole either assigns 1 lie to each element of A or to each element of [n] \ A. Paul wins the regular (resp. pathological) game if after q rounds there is at least one (resp. at most one) element with one or fewer l...

In this paper, some local and parallel discretizations and adaptive finite element algorithms are proposed and analyzed for nonlinear elliptic boundary value problems in both two and three dimensions. The main technique is to use a standard finite element discretization on a coarse grid to approximate low frequencies and then to apply some linearized discretization on a fine grid to correct the...

This paper completes the classification of central extensions of three dimensional Artin-Schelter regular algebras to four dimensional Artin-Schelter regular algebras. Let A be an AS regular algebra of global dimension three and let D be an extension of A by a central graded element z, i.e. D/〈z〉 = A. If A is generated by elements of degree one, those algebras D which are again AS regular have ...