An equilibrated flux a posteriori error estimator for defeaturing problems
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We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance ...
This thesis is devoted to the derivation of error estimates for partial differential equations with random input data, with a focus on a posteriori error estimates which are the basis for adaptive strategies. Such procedures aim at obtaining an approximati ...
A reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) for a class of nonlinear homogenization elliptic problems of nonmonotone type is introduced. In this approach, the solutions of the micro problems needed to estimate the macroscopic ...
This work is concerned with the estimation of the spreading potential of the disease in the initial stages of an epidemic. A speedy and accurate estimation is important for determining whether or not interventions are necessary to prevent a major outbreak. ...
This work is devoted to an adaptive multiscale finite element method (MsFEM) for solving elliptic problems with rapidly oscillating coefficients. Starting from a general version of the MsFEM with oversampling, we derive an a posteriori estimate for the H-1 ...
We develop a new reduced basis (RB) method for the rapid and reliable approximation of parametrized elliptic eigenvalue problems. The method hinges upon dual weighted residual type a posteriori error indicators which estimate, for any value of the paramete ...
In this paper, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a para ...
This paper proposes a tradeoff between sample complexity and computation time that applies to statistical estimators based on convex optimization. As the amount of data increases, we can smooth optimization problems more and more aggressively to achieve ac ...
This work provides a review on reduced order methods in solving uncertainty quantification problems. A quick introduction of the reduced order methods, including proper orthogonal decomposition and greedy reduced basis methods, are presented along with the ...
We develop a new reduced basis (RB) method for the rapid and reliable approximation of parametrized elliptic eigenvalue problems. The method hinges upon dual weighted residual type a posteriori error indicators which estimate, for any value of the paramete ...