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We introduce new Godunov-type semidiscrete central schemes for hyperbolic systems of conservation laws and Hamilton–Jacobi equations. The schemes are based on the use of more precise information about the local speeds of propagation and can be viewed as a generalization of the schemes from [A. A third-order semidiscrete genuinely multidimensional central(More)
Let Φ(ω), ω ∈ Ω, be a family of n × N random matrices whose entries φ i,j are independent realizations of a symmetric, real random variable η with expectation IEη = 0 and variance IEη 2 = 1/n. Such matrices are used in compressed sensing to encode a vector x ∈ IR N by y = Φx. The information y holds about x is extracted by using a decoder ∆ : IR n → IR N.(More)
The reduced basis method was introduced for the accurate online evaluation of solutions to a parameter dependent family of elliptic partial differential equations. Abstractly, it can be viewed as determining a " good " n dimensional space H n to be used in approximating the elements of a compact set F in a Hilbert space H. One, by now popular, computational(More)
Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n dimensional space X n ⊂ X which can be used to approximate the elements of F. The best possible error we can achieve for such an approximation is given by the Kolmogorov width d n (F) X. However, finding the space which gives this performance is typically(More)
We consider a novel second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids which was originally introduced in [3]. Here, in several numerical experiments we demonstrate accuracy, high resolution and robustness of the proposed method. We consider the two-dimensional (2-D) Saint-Venant system of shallow(More)
Let f be a continuous function defined on Ω := [0, 1] N which depends on only coordinate variables, f x i). We assume that we are given m and are allowed to ask for the values of f at m points in Ω. If g is in Lip1 and the coordinates i 1 ,. .. , i are known to us, then by asking for the values of f at m = L uniformly spaced points, we could recover f to(More)
A family of Godunov-type central-upwind schemes for the Saint-Venant system of shallow water equations has been first introduced in [A. Depending on the reconstruction step, the second-order versions of the schemes there could be made either well-balanced or positivity preserving, but fail to satisfy both properties simultaneously. Here, we introduce an(More)
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves stationary steady states (lake at rest) and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular(More)