A Priori Error Estimate of Deep Mixed Residual Method for Elliptic PDEs
Journal of Scientific ComputingIn this work, we derive a priori error estimate of the mixed residual method when solving some elliptic PDEs. Our work is the first theoretical study of this method. We prove that the neural network solutions will converge if we increase the training samples and network size without any constraint on the ratio of training samples to the network size ...
Lingfeng Li +3 more
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A priori error indicator in the transformation method for problems with geometric uncertainties [PDF]
, 2013 Version éditeur de cette publication à l'adresse suivante : http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6514655To solve stochastic problems with geometric uncertainties, one can transform the original problem in a domain with stochastic ...
Mac, Duc Hung +4 more
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The a priori estimate of the maximum modulus to solutions of doubly nonlinear parabolic equations [PDF]
, 1997 summary:The a priori estimate of the maximum modulus of the generalized solution is established for a doubly nonlinear parabolic equation with special structural ...
Zaide, Wu, Liang, Xiting,
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Hyperparameter estimation for uncertainty quantification in mesoscale carbon dioxide inversions
Tellus: Series B, Chemical and Physical Meteorology, 2013 Uncertainty quantification is critical in the inversion of CO2 surface fluxes from atmospheric concentration measurements. Here, we estimate the main hyperparameters of the error covariance matrices for a priori fluxes and CO2 concentrations, that is ...
Lin Wu +4 more
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A priori error estimation of the structure-preserving modal model reduction by state residualization of a grid forming converter for use in 100% power electronics transmission systems [PDF]
, 2019 This article deals with the model order reduction by state residualization of power electronic converters. It presents a method to a priori estimate the error induced by this reduction.
COLAS, Frédéric +2 more
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A Priori and a Posteriori Error Analysis for a Linear Elliptic Problem with Dynamic Boundary Condition [PDF]
, 2015 In this paper, we study the time dependent linear elliptic problem with dynamic boundary condition. The problem is discretized by the backward Euler’s scheme in time and finite elements in space.
Sayah, Toni +2 more
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Nonlinear Analysis, 2014 We consider the Poisson equation in a rectangular domain. Instead of the classical specification of boundary data, we impose an integral constraints on the inner stripe adjacent to boundary having the width ξ.
Givi Berikelashvilia, Nodar Khomeriki
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Understanding Statistical Testing
SAGE Open, 2015 Statistical hypothesis testing is common in research, but a conventional understanding sometimes leads to mistaken application and misinterpretation.
Peter J. Veazie
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hp-FEM for the $$\alpha $$-Mosolov problem: a priori and a posteriori error estimates
Numerische MathematikAbstractAn hp-finite element discretization for the $$\alpha $$ α -Mosolov problem, a scalar variant of the Bingham flow problem but with the $$\alpha $$ α -Laplacian operator, is being analyzed.
Lothar Banz, Ernst P. Stephan
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A Priori Error Estimate of a Discontinuous Finite Volume Method for the Obstacle Problem
Asia Pacific Journal of Mathematics, 2021 Yuping Zeng, Ting Li
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