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An error estimate for Volterra integral equations
Springer Science and Business Media LLC - - 1971
G. M. Phillips
An application of Chawla's identity to a different scheme for singular problems
Springer Science and Business Media LLC - Tập 30 - Trang 566-568 - 1990
Manabu Sakai, Riaz A. Usmani
Two new approaches for solving elliptic obstacle problems using discontinuous Galerkin methods
Springer Science and Business Media LLC - Tập 62 - Trang 89-124 - 2021
Sharat Gaddam, Thirupathi Gudi, Kamana Porwal
The main aim of this article is to present two new ways to solve the elliptic obstacle problem by using discontinuous Galerkin finite element methods. In Gaddam and Gudi (Comput Methods Appl Math 18:223–236, 2018. https://doi.org/10.1515/cmam-2017-0018...... hiện toàn bộ
Accurate discretization of poroelasticity without Darcy stability
Springer Science and Business Media LLC - Tập 61 - Trang 941-976 - 2021
Kent-Andre Mardal, Marie E. Rognes, Travis B. Thompson
In this manuscript we focus on the question: what is the correct notion of Stokes–Biot stability? Stokes–Biot stable discretizations have been introduced, independently by several authors, as a means of discretizing Biot’s equations of poroelasticity; such schemes retain their stability and convergence properties, with respect to appropriately defined norms, in the context of a vanishing storage c...... hiện toàn bộ
A simplified HSS preconditioner for generalized saddle point problems
Springer Science and Business Media LLC - Tập 56 - Trang 423-439 - 2015
Yang Cao, Zhi-Ru Ren, Quan Shi
For generalized saddle point problems, we propose a simplified Hermitian and skew-Hermitian splitting (SHSS) preconditioner which is much closer to the generalized saddle point matrix than the HSS preconditioner. It is proved that all eigenvalues of the SHSS preconditioned matrix are real and nonunit eigenvalues are located in a positive interval. We also study the eigenvector distribution and the...... hiện toàn bộ
Parallel Newton Two-Stage Multisplitting Iterative Methods for Nonlinear Systems
Springer Science and Business Media LLC - Tập 43 - Trang 849-861 - 2003
Josep Arnal, Violeta Migallón, José Penadés
Parallel Newton two-stage iterative methods to solve nonlinear systems are studied. These algorithms are based on both the multisplitting technique and the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms studied, computational results ab...... hiện toàn bộ
Fractional Tikhonov regularization for linear discrete ill-posed problems
Springer Science and Business Media LLC - Tập 51 - Trang 197-215 - 2011
Michiel E. Hochstenbach, Lothar Reichel
Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A. This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residual error (discrepancy) in Tikhonov regularization with a seminorm that uses a fractional power of the...... hiện toàn bộ
Các Ước Lượng Aubin—Nitsche Tương Đương Với Các Nhúng Chặt Dịch bởi AI
Springer Science and Business Media LLC - Tập 44 - Trang 287-290 - 2004
Francisco-Javier Sayas
Trong ghi chú ngắn này, chúng tôi chỉ ra rằng việc có một ước lượng loại Aubin–Nitsche (một ước lượng siêu hội tụ trong một chuẩn yếu hơn cho một phương pháp Galerkin hội tụ) là tương đương với việc có nhúng chặt của không gian vào không gian hoàn thành của nó với chuẩn yếu hơn.
#Aubin–Nitsche #ước lượng #nhúng chặt #phương pháp Galerkin #hội tụ
Optimal quadratures for analytic functions
Springer Science and Business Media LLC - Tập 12 - Trang 489-502 - 1972
M. M. Chawla, B. L. Raina
For integrals∫ −1 1 w(x)f(x)dx with $$w(x) = (1 - x)^{ \pm \tfrac{1}{2}} (1 + x)^{ \pm \tfrac{1}{2}} $$ and with analytic integrands, we consider the determination of “optimal” abscissasx ...... hiện toàn bộ
A fractional Adams–Simpson-type method for nonlinear fractional ordinary differential equations with non-smooth data
Springer Science and Business Media LLC - Tập 63 - Trang 1-40 - 2023
Yuan-Ming Wang, Bo Xie
We propose a fractional Adams–Simpson-type method for nonlinear fractional ordinary differential equations with fractional order $$\alpha \in (0,1)$$ . In our method, a nonuniform mesh is used so that the optimal convergence order can be recovered for non-smooth data. By developing a modified fract...... hiện toàn bộ
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