Mixed Schemes for Fourth-Order DIV Equations

2019 ◽  
Vol 19 (2) ◽  
pp. 341-357
Author(s):  
Ronghong Fan ◽  
Yanru Liu ◽  
Shuo Zhang
Keyword(s):  
Theoretical Analysis ◽  
Fourth Order ◽  
Convergence Rates ◽  
Mixed Formulation ◽  
Optimal Convergence ◽  
Mixed Formulations ◽  
Optimal Convergence Rates

AbstractIn this paper, stable mixed formulations are designed and analyzed for the quad div problems under two frameworks presented in [23] and [22], respectively. Analogue discretizations are given with respect to the mixed formulation, and optimal convergence rates are observed, which confirm the theoretical analysis.

scholarly journals Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 221
Author(s):  
Rong Zhang ◽  
Fanchun Li ◽  
Xingjun Luo
Keyword(s):  
Theoretical Analysis ◽  
Galerkin Method ◽  
Integral Equations ◽  
Convergence Rates ◽  
Numerical Results ◽  
Compression Algorithm ◽  
Optimal Convergence ◽  
Relaxation Factor ◽  
Optimal Convergence Rates ◽  
Ill Posed

In this paper, Landweber iteration with a relaxation factor is proposed to solve nonlinear ill-posed integral equations. A compression multiscale Galerkin method that retains the properties of the Landweber iteration is used to discretize the Landweber iteration. This method leads to the optimal convergence rates under certain conditions. As a consequence, we propose a multiscale compression algorithm to solve nonlinear ill-posed integral equations. Finally, the theoretical analysis is verified by numerical results.

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