scholarly journals Optimal error estimate for a space-time discretization for incompressible generalized Newtonian fluids: the Dirichlet problem

2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Luigi C. Berselli ◽  
Michael Růžička
Keyword(s):  
Time Discretization ◽  
Unsteady Motion ◽  
Space Time ◽  
Dirichlet Boundary Conditions ◽  
Optimal Error Estimates ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Shear Thinning Fluids ◽  
Discrete Problems ◽  
Homogeneous Dirichlet Boundary Conditions

AbstractIn this paper we prove optimal error estimates for solutions with natural regularity of the equations describing the unsteady motion of incompressible shear-thinning fluids. We consider a full space-time semi-implicit scheme for the discretization. The main novelty, with respect to previous results, is that we obtain the estimates directly without introducing intermediate semi-discrete problems, which enables the treatment of homogeneous Dirichlet boundary conditions.

scholarly journals Space–time discretization for nonlinear parabolic systems with p-structure

2020 ◽  
Author(s):  
Luigi C Berselli ◽  
Michael Růžička
Keyword(s):  
Time Discretization ◽  
Parabolic Systems ◽  
Dirichlet Boundary Conditions ◽  
Optimal Error Estimates ◽  
Nonlinear Parabolic Systems ◽  
Optimal Error ◽  
Nonlinear Parabolic ◽  
Symmetric Gradient ◽  
Homogeneous Dirichlet Boundary Conditions ◽  
Continuous Problem

Abstract In this paper we consider nonlinear parabolic systems with elliptic part, depending only on the symmetric gradient, which can be also degenerate. We prove optimal error estimates for solutions with natural regularity. The main novelty, with respect to previous results, is that we obtain the estimates directly without introducing intermediate semidiscrete problems, which enables the treatment of homogeneous Dirichlet boundary conditions. In addition, we prove the existence of solutions of the continuous problem with the requested regularity, if the data of the problem are smooth enough.

Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models

2013 ◽  
Vol 3 (1) ◽  
pp. 59-80 ◽  
Author(s):  
Xinlong Feng ◽  
Tao Tang ◽  
Jiang Yang
Keyword(s):  
Numerical Experiments ◽  
Time Discretization ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Fully Discrete ◽  
Phase Field Models ◽  
Discretization Schemes ◽  
Energy Stable ◽  
Theoretical Results ◽  
Crank Nicolson

AbstractIn this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented for the Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed time discretization schemes are either unconditionally energy stable, or conditionally energy stable under some reasonable stability conditions. Optimal error estimates for the semi-discrete schemes and fully-discrete schemes will be derived. Numerical experiments are carried out to demonstrate the theoretical results.

scholarly journals Optimal Error Estimate of Chebyshev-Legendre Spectral Method for the Generalised Benjamin-Bona-Mahony-Burgers Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Tinggang Zhao ◽  
Xiaoxian Zhang ◽  
Jinxia Huo ◽  
Wanghui Su ◽  
Yongli Liu ◽  
...  
Keyword(s):  
Error Estimate ◽  
Spectral Method ◽  
Time Discretization ◽  
Stability And Convergence ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Legendre Spectral Method ◽  
Leapfrog Scheme ◽  
Set Up ◽  
The Stability

Combining with the Crank-Nicolson/leapfrog scheme in time discretization, Chebyshev-Legendre spectral method is applied to space discretization for numerically solving the Benjamin-Bona-Mahony-Burgers (gBBM-B) equations. The proposed approach is based on Legendre Galerkin formulation while the Chebyshev-Gauss-Lobatto (CGL) nodes are used in the computation. By using the proposed method, the computational complexity is reduced and both accuracy and efficiency are achieved. The stability and convergence are rigorously set up. Optimal error estimate of the Chebyshev-Legendre method is proved for the problem with Dirichlet boundary condition. The convergence rate shows “spectral accuracy.” Numerical experiments are presented to demonstrate the effectiveness of the method and to confirm the theoretical results.

Optimal Error Estimates for Semi–implicit DG Time Discretization of Convection–Diffusion Problems

2011 ◽  
Author(s):  
Miloslav Vlasák ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
Zacharias Anastassi
Keyword(s):  
Error Estimates ◽  
Time Discretization ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Convection Diffusion ◽  
Diffusion Problems

scholarly journals A stabilized coupled method and its optimal error estimates for elliptic interface problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jiaping Yu ◽  
Feng Shi ◽  
Jianping Zhao
Keyword(s):  
Error Estimates ◽  
Numerical Experiments ◽  
Interface Problems ◽  
Optimal Error Estimates ◽  
Computational Stability ◽  
Optimal Error ◽  
Stabilized Method ◽  
Elliptic Interface Problems ◽  
Coupled Method

Abstract In this paper, we present a stabilized coupled algorithm for solving elliptic interface problems, mainly by introducing the jump of the solutions along the interface. A framework of theoretical proofs is provided to show the optimal error estimates of this stabilized method. Several numerical experiments are carried out to demonstrate the computational stability and effectiveness of the method.

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