INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces
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Many applied problems, like transport processes in porous media or ferromagnetism in composite materials, can be modeled by partial differential equations (PDEs) with heterogeneous coefficients that rapidly vary at small scales. To capture the effective be ...
Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...
Isogeometric Analysis (IGA) is a computational methodology for the numerical approximation of Partial Differential Equations (PDEs). IGA is based on the isogeometric concept, for which the same basis functions, usually Non-Uniform Rational B-Splines (NURBS ...
We are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used ...
In this paper we propose a rescaled localized radial basis function (RL-RBF) interpolation method, based on the use of compactly supported radial basis functions. Starting from the classical RBF interpolation technique, we introduce a rescaling that allows ...
The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For s ...
In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...
In this work we provide a convergence analysis for the quasi-optimal version of the Stochastic Sparse Grid Collocation method we had presented in our previous work \On the optimal polynomial approximation of Stochastic PDEs by Galerkin and Collocation meth ...
We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitate ...
In this paper, we focus on the problem of interpolating a continuous-time AR(1) process with stable innovations using minimum average error criterion. Stable innovations can be either Gaussian or non-Gaussian. In the former case, the optimality of the expo ...