This work develops an ε-uniform finite element method for singularly perturbed two-point boundary value problems. A surprising and remarkable observation is illustrated: By inserting one node arbitrarily in any element, the new finite element solution always intersects with the original one at fixed points, and the errors at those points converge at the same rate as regular boundary value probl...

We present a range of mesh-dependent inequalities for piecewise constant and continuous piecewise linear nite element functions u deened on locally reened shape-regular (but possibly non-quasiuniform) meshes. These inequalities involve norms of the form kh uk W s;p (() for positive and negative s and , where h is a function which reeects the local mesh diameter in an appropriate way. The only g...

We propose a stabilized subgrid finite-element method for the two-dimensional 2D nonstationary incompressible Naver-Stokes equation NSE . This method yields a subgrid eddy viscosity which does not act on the large flow structures. The proposed eddy viscous term is constructed by a fluctuation operator based on an L2-projection. The fluctuation operator can be implemented by the L2-projection fr...

class RSO extends ElementCollection { val speed: Element[Double] val amr: Element[Symbol] val attitude: Element[Symbol] val spin: Element[Symbol] val shape: Element[Symbol] } class Payload extends RSO { val amr: Element[Symbol] = Select(0.9 -> 'low, 0.1 -> 'medium, 0.0 -> 'high)("amr", this) val attitude: Element[Symbol] = Select(0.5 -> 'uncontrolled, 0.5 -> 'controlled)("attitude", this) val s...

We show the intimate connection between various mathematical notions that are currently under active investigation: a class of Garside monoids, with a “nice” Garside element, certain monoids S with quadratic relations, whose monoidal algebra A = kS has a Frobenius Koszul dual A with regular socle, the monoids of skew-polynomial type (or equivalently, binomial skew-polynomial rings) which were i...

In this paper we present a graph grammar based direct solver algorithm for hp-adaptive finite element method simulations with point singularities. The solver algorithm is obtained by representing computational mesh as a graph and prescribing the solver algorithm by graph grammar productions. Classical direct solvers deliver O(Np+N) computational cost for regular 2D grids, and O(Np+N) for regula...

If a ring element α = 1 − ab is Drazin invertible, so is β = 1 − ba. We show that the Drazin inverse of β is expressible by a simple formula (in generalization of “Jacobson’s Lemma”) in terms of the Drazin inverse and the spectral idempotent of α. The commutation rules αa = a β and b α = β b are extended to the Drazin inverses, and the spectral idempotents of α and β are shown to be isomorphic....