An efficient spectral method and rigorous error analysis based on dimension reduction scheme for fourth order problems

2020 ◽  
Vol 37 (1) ◽  
pp. 152-171
Author(s):  
Lan Li ◽  
Jing An
Keyword(s):  
Error Analysis ◽  
Dimension Reduction ◽  
Spectral Method ◽  
Fourth Order ◽  
Reduction Scheme ◽  
Rigorous Error ◽  
Fourth Order Problems

A Spectral Method for Second Order Volterra Integro-Differential Equation with Pantograph Delay

2013 ◽  
Vol 5 (2) ◽  
pp. 131-145 ◽  
Author(s):  
Weishan Zheng ◽  
Yanping Chen
Keyword(s):  
Differential Equation ◽  
Error Analysis ◽  
Rate Of Convergence ◽  
Spectral Method ◽  
Second Order ◽  
Integro Differential Equation ◽  
Collocation Spectral Method ◽  
Rigorous Error

AbstractIn this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with pantograph delay. We provide a rigorous error analysis for the proposed method. The spectral rate of convergence for the proposed method is established in both L2-norm and L∞-norm.

scholarly journals Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients

2021 ◽  
Author(s):  
Andreas Dedner ◽  
Alice Hodson
Keyword(s):  
Fourth Order ◽  
Perturbation Parameter ◽  
Two Dimensions ◽  
Optimal Error Estimates ◽  
Projection Operators ◽  
Varying Coefficients ◽  
Virtual Element Methods ◽  
Virtual Element ◽  
Perturbation Problems ◽  
Fourth Order Problems

Abstract We present a class of nonconforming virtual element methods for general fourth-order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element spaces. Optimal error estimates in the energy norm are provided for general linear fourth-order problems with varying coefficients. We also discuss fourth-order perturbation problems and present a novel nonconforming scheme which is uniformly convergent with respect to the perturbation parameter without requiring an enlargement of the space. Numerical tests are carried out to verify the theoretical results. We conclude with a brief discussion on how our approach can easily be applied to nonlinear fourth-order problems.

Sign in / Sign up

Export Citation Format

Share Document