scholarly journals Approximation Error Analysis of Some Deep Backward Schemes for Nonlinear PDEs

2022 ◽  
Vol 44 (1) ◽  
pp. A28-A56
Author(s):  
Maximilien Germain ◽  
Huyên Pham ◽  
Xavier Warin
Keyword(s):  
Error Analysis ◽  
Approximation Error ◽  
Nonlinear Pdes

scholarly journals An integral equation formulation of the N-body dielectric spheres problem. Part 1: Numerical analysis

2020 ◽  
Author(s):  
Muhammad Hassan ◽  
Benjamin Stamm
Keyword(s):  
Integral Equation ◽  
Numerical Analysis ◽  
Error Analysis ◽  
Convergence Rates ◽  
A Priori ◽  
Approximation Error ◽  
Spherical Particles ◽  
Integral Equation Formulation ◽  
Dielectric Spheres ◽  
The Stability

In this article, we analyse an integral equation of the second kind that represents the solution of N interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the stability constants- and thus the approximation error- with respect to the number N of involved dielectric spheres. We develop a new a priori error analysis that demonstrates N-independent stability of the continuous and discrete formulations of the integral equation. Consequently, we obtain convergence rates that are independent of N.

scholarly journals Approximate conversion of Bézier curves

1995 ◽  
Vol 51 (1) ◽  
pp. 153-162 ◽  
Author(s):  
Yungeom Park ◽  
U Jin Choi ◽  
Ha-Jine Kimn
Keyword(s):  
Error Analysis ◽  
A Priori ◽  
Approximation Error ◽  
Bézier Curve ◽  
Bezier Curve ◽  
A Priori Bounds ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Geometric Properties

The methods for generating a polynomial Bézier approximation of degree n − 1 to an nth degree Bézier curve, and error analysis, are presented. The methods are based on observations of the geometric properties of Bézier curves. The approximation agrees at the two endpoints up to a preselected smoothness order. The methods allow a detailed error analysis, providing a priori bounds of the point-wise approximation error. The error analysis for other authors’ methods is also presented.

scholarly journals Error estimates for a multidimensional meshfree Galerkin method with diffuse derivatives and stabilization

2013 ◽  
Vol 9 (17) ◽  
pp. 53-76
Author(s):  
Mauricio Osorio ◽  
Donald French
Keyword(s):  
Differential Equation ◽  
Convergence Rate ◽  
Error Analysis ◽  
Boundary Conditions ◽  
Galerkin Method ◽  
Approximation Error ◽  
Neumann Boundary ◽  
Meshfree Method ◽  
General Elliptic ◽  
Better Than

A meshfree method with diffuse derivatives and a penalty stabilization is developed. An error analysis for the approximation of the solution of a general elliptic differential equation, in several dimensions, with Neumann boundary conditions is provided. Theoretical and numerical results show that the approximation error and the convergence rate are better than the diffuse element method.

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