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Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes

Martin Vohralík (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the lowest-order Raviart–Thomas mixed finite element method for second-order elliptic problems on simplicial meshes in two and three space dimensions. This method produces saddle-point problems for scalar and flux unknowns. We show how to easily and locally eliminate the flux unknowns, which implies the equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration. The matrix of the final linear system is sparse, positive...

Equivalence of compositional expressions and independence relations in compositional models

Francesco M. Malvestuto (2014)

Kybernetika

We generalize Jiroušek’s (right) composition operator in such a way that it can be applied to distribution functions with values in a “semifield“, and introduce (parenthesized) compositional expressions, which in some sense generalize Jiroušek’s “generating sequences” of compositional models. We say that two compositional expressions are equivalent if their evaluations always produce the same results whenever they are defined. Our first result is that a set system is star-like with centre X if...

Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere

Ľubomír Baňas, Zdzisław Brzeźniak, Mikhail Neklyudov, Martin Ondreját, Andreas Prohl (2015)

Czechoslovak Mathematical Journal

We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering only solutions which are independent of the space variable. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and obtain also results on attractivity towards an invariant measure. We also...

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