ﻻ يوجد ملخص باللغة العربية
We propose and study an iterative substructuring method for an h-p Nitsche-type discretization, following the original approach introduced in [Bramble, Pasciack, Schatz (Math Comp. 1986)] for conforming methods. We prove quasi-optimality with respect to the mesh size and the polynomial degree for the proposed preconditioner. Numerical experiments asses the performance of the preconditioner and verify the theory.
In this paper, we propose a deep unfitted Nitsche method for computing elliptic interface problems with high contrasts in high dimensions. To capture discontinuities of the solution caused by interfaces, we reformulate the problem as an energy minimi
We propose a new method to deal with the essential boundary conditions encountered in the deep learning-based numerical solvers for partial differential equations. The trial functions representing by deep neural networks are non-interpolatory, which
The Sinc-Nystr{o}m method in time is a high-order spectral method for solving evolutionary differential equations and it has wide applications in scientific computation. But in this method we have to solve all the time steps implicitly at one-shot, w
In this corrigendum, we offer a correction to [J. Korean. Math. Soc., 54 (2017), pp. 461--477]. We construct a counterexample for the strengthened Cauchy--Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5
In this paper, several projection method based preconditioners for various incompressible flow models are studied. In particular, we are interested in the theoretical analysis of a pressure-correction projection method based preconditioner cite{griff