A Generalized Lax-Milgram Theorem

The Lax-Milgram Theorem. A detailed proof to be formalized in Coq

To guarantee the correction of numerical simulation programs implementing the fi-nite element method, it is necessary to formalize the mathematical notions and results that allowto establish the soundness of the method. The Lax-Milgram theorem is one of those theoreticalcornerstones: under some completeness and coercivity assumptions, it states existence and unique-ness of the s...

Generalized Foldy-Lax formulation

We present a method for numerical wave propagation in a heterogeneous medium. The medium is defined in terms of an extended scatterer or target which is surrounded by many small scatterers. By extending the classic Foldy-Lax formulation we developed an efficient algorithm for numerical wave propagation in two dimension. In the method that we set forth multiple scattering among the point scatter...

A Fixed Point Theorem in Generalized D-metric Spaces

Lax theorem and finite volume schemes

This work addresses a theory of convergence for finite volume methods applied to linear equations. A non-consistent model problem posed in an abstract Banach space is proved to be convergent. Then various examples show that the functional framework is non-empty. Convergence with a rate h 1 2 of all TVD schemes for linear advection in 1D is an application of the general result. Using duality tec...

Generalized lax Veronesean embeddings of projective spaces

We classify all embeddings θ : PG(n,K) −→ PG(d,F), with d ≥ n(n+3) 2 and K,F skew fields with |K| > 2, such that θ maps the set of points of each line of PG(n,K) to a set of coplanar points of PG(d,F), and such that the image of θ generates PG(d,F). It turns out that d = 12n(n+ 3) and all examples “essentially” arise from a similar “full” embedding θ′ : PG(n,K) −→ PG(d,K) by identifying K with ...