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Kansa-RBF algorithms for elliptic problems in regular polygonal domains
(2018)
We propose matrix decomposition algorithms for the efficient solution of the linear systems arising from Kansa radial basis function discretizations of elliptic boundary value problems in regular polygonal domains. These ...
Prediction of catastrophes in space over time
(2018)
Predicting rare events, such as high level up-crossings, for spatio-temporal processes plays an important role in the analysis of the occurrence and impact of potential catastrophes in, for example, environmental settings. ...
Shape parameter estimation in RBF function approximation
(2019)
The radial basis function (RBF) collocation method is applied for the approximation of functions in two variables. When the RBFs employed include a shape parameter, the determination of an appropriate value for it is a ...
Determination of shape parameter in RBF approximation
(WIT Press, 2019)
We apply a radial basis function (RBF) collocation method for the approximation of functions in two dimensions. The solution is approximated by a linear combination of radial basis functions. The issue of determining the ...
Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems
(2018)
We consider the inverse problem of recovering an unknown functional parameter in a separable Banach space, from a noisy observation vector of its image through a known possibly non-linear map . We adopt a Bayesian approach ...
Self-inverse and exchangeable random variables
(2013)
A random variable Z will be called self-inverse if it has the same distribution as its reciprocal Z -1. It is shown that if Z is defined as a ratio, X / Y, of two rv's X and Y (with P[X=0]=P[Y=0]=0), then Z is self-inverse ...
Finite element approximation of reaction–diffusion problems using an exponentially graded mesh
(2018)
We present the analysis of an h version Finite Element Method for the approximation of the solution to singularly perturbed reaction–diffusion problems posed in smooth domains Ω⊂R2. The method uses piecewise polynomials ...
On the regularity of the non-dynamic parabolic fractional obstacle problem
(2018)
In the class of the non-dynamic Fractional Obstacle Problems of parabolic type, it is shown existence, uniqueness, apriori bounds of the solution and optimal regularity of the space derivatives of the solution. Furthermore, ...
Parabolic Obstacle Problems. Quasi-convexity and Regularity
(2019)
In a wide class of the so called Obstacle Problems of parabolic type it is shown how to improve the optimal regularity of the solution and as a consequence how to obtain space-time regularity of the corresponding free boundary.