Quasi-Optimal Pointwise Error Estimates for the Reissner–Mindlin Plate

1991 ◽  
Vol 28 (2) ◽  
pp. 363-377 ◽  
Author(s):  
Lucia Gastaldi ◽  
Ricardo H. Nochetto
Keyword(s):  
Error Estimates ◽  
Mindlin Plate ◽  
Pointwise Error ◽  
Pointwise Error Estimates

scholarly journals Two-scale method for the Monge–Ampère equation: pointwise error estimates

2018 ◽  
Vol 39 (3) ◽  
pp. 1085-1109 ◽  
Author(s):  
R H Nochetto ◽  
D Ntogkas ◽  
W Zhang
Keyword(s):  
Error Estimates ◽  
Viscosity Solution ◽  
Continuous Dependence ◽  
Convergence Rates ◽  
Classical Solutions ◽  
Discrete Version ◽  
Scale Method ◽  
Pointwise Error ◽  
Pointwise Error Estimates ◽  
Monge Ampere

Abstract In this paper we continue the analysis of the two-scale method for the Monge–Ampère equation for dimension d ≥ 2 introduced in the study by Nochetto et al. (2017, Two-scale method for the Monge–Ampère equation: convergence to the viscosity solution. Math. Comput., in press). We prove continuous dependence of discrete solutions on data that in turn hinges on a discrete version of the Alexandroff estimate. They are both instrumental to prove pointwise error estimates for classical solutions with Hölder and Sobolev regularity. We also derive convergence rates for viscosity solutions with bounded Hessians which may be piecewise smooth or degenerate.

Localized pointwise error estimates for direct flux approximation

2015 ◽  
Vol 36 (3) ◽  
pp. 1410-1431
Author(s):  
JaEun Ku
Keyword(s):  
Error Estimates ◽  
Pointwise Error ◽  
Flux Approximation ◽  
Pointwise Error Estimates

Pointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems

2013 ◽  
Vol 13 (1) ◽  
pp. 79-94 ◽  
Author(s):  
Huiqing Zhu ◽  
Zhimin Zhang
Keyword(s):  
Error Estimates ◽  
Reaction Diffusion ◽  
Local Discontinuous Galerkin Method ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
One Dimensional ◽  
Pointwise Error ◽  
Ldg Method ◽  
Pointwise Error Estimates ◽  
Diffusion Problems

Abstract. The local discontinuous Galerkin method (LDG) is considered for solving one-dimensional singularly perturbed two-point boundary value problems of reaction-diffusion type. Pointwise error estimates for the LDG approximation to the solution and its derivative are established on a Shishkin-type mesh. Numerical experiments are presented. Moreover, a superconvergence of order of the numerical traces is observed numerically.

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