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Quasi-A Priori Truncation Error Estimation in the DGSEM
Springer Science and Business Media LLC - Tập 64 - Trang 425-455 - 2014
Gonzalo Rubio, François Fraysse, David A. Kopriva, Eusebio Valero
In this paper we show how to accurately perform a quasi-a priori estimation of the truncation error of steady-state solutions computed by a discontinuous Galerkin spectral element method. We estimate the spatial truncation error using the $$\tau $$ ...... hiện toàn bộ
A Homotopy Method for Parameter Estimation of Nonlinear Differential Equations with Multiple Optima
Springer Science and Business Media LLC - Tập 74 - Trang 1314-1324 - 2017
Wenrui Hao
A numerical method for estimating multiple parameter values of nonlinear systems arising from biology is presented. The uncertain parameters are modeled as random variables. Then the solutions are expressed as convergent series of orthogonal polynomial expansions in terms of the input random parameters. Homotopy continuation method is employed to solve the resulting polynomial system, and more imp...... hiện toàn bộ
Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations
Springer Science and Business Media LLC - Tập 70 - Trang 407-428 - 2015
Yanmin Zhao, Pan Chen, Weiping Bu, Xiangtao Liu, Yifa Tang
Based on spatial conforming and nonconforming mixed finite element methods combined with classical L1 time stepping method, two fully-discrete approximate schemes with unconditional stability are first established for the time-fractional diffusion equation with Caputo derivative of order $$0<\alpha <1$$ ...... hiện toàn bộ
Second Order, Unconditionally Stable, Linear Ensemble Algorithms for the Magnetohydrodynamics Equations
Springer Science and Business Media LLC - Tập 94 - Trang 1-29 - 2023
John Carter, Daozhi Han, Nan Jiang
We propose two unconditionally stable, linear ensemble algorithms with pre-computable shared coefficient matrices across different realizations for the magnetohydrodynamics equations. The viscous terms are treated by a standard perturbative discretization. The nonlinear terms are discretized fully explicitly within the framework of the generalized positive auxiliary variable approach (GPAV). Artif...... hiện toàn bộ
Development of a Variational Multiscale Large-Eddy Simulation Code ‘MISTRAL’ Using Double-Scale Finite Elements
Springer Science and Business Media LLC - Tập 43 - Trang 433-453 - 2008
Yuzuru Eguchi
A variational multiscale large-eddy simulation (VMS-LES) code, named MISTRAL, has been developed based upon the finite element method (FEM) for accurate and practical computation of geometrically complicated turbulent flow problems. The numerical strategy of the FEM-based VMS-LES is explained, especially focusing on the double-scale approximation for velocity and pressure in the incompressible Nav...... hiện toàn bộ
Computations of Optimal Transport Distance with Fisher Information Regularization
Springer Science and Business Media LLC - Tập 75 - Trang 1581-1595 - 2017
Wuchen Li, Penghang Yin, Stanley Osher
We propose a fast algorithm to approximate the optimal transport distance. The main idea is to add a Fisher information regularization into the dynamical setting of the problem, originated by Benamou and Brenier. The regularized problem is shown to be smooth and strictly convex, thus many classical fast algorithms are available. In this paper, we adopt Newton’s method, which converges to the minim...... hiện toàn bộ
Convergence of Summation-by-Parts Finite Difference Methods for the Wave Equation
Springer Science and Business Media LLC - Tập 71 - Trang 219-245 - 2016
Siyang Wang, Gunilla Kreiss
When using a finite difference method to solve a time dependent partial differential equation, the truncation error is often larger at a few grid points near a boundary or grid interface than in the interior. In computations, the observed convergence rate is often higher than the order of the large truncation error. In this paper, we develop techniques for analyzing this phenomenon, and particular...... hiện toàn bộ
Supercloseness of Primal-Dual Galerkin Approximations for Second Order Elliptic Problems
Springer Science and Business Media LLC - Tập 75 - Trang 376-394 - 2017
Bernardo Cockburn, Manuel A. Sánchez, Chunguang Xiong
We show that two widely used Galerkin formulations for second-order elliptic problems provide approximations which are actually superclose, that is, their difference converges faster than the corresponding errors. In the framework of linear elasticity, the two formulations correspond to using either the stiffness tensor or its inverse the compliance tensor. We find sufficient conditions, for a wid...... hiện toàn bộ
A High-Order Method with a Temporal Nonuniform Mesh for a Time-Fractional Benjamin–Bona–Mahony Equation
Springer Science and Business Media LLC - - 2019
Pin Lyu, Seakweng Vong
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Springer Science and Business Media LLC - Tập 16 - Trang 173-261 - 2001
Bernardo Cockburn, Chi-Wang Shu
In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge–Kutta time discretizations, that allows the meth...... hiện toàn bộ
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