抛物积分微分方程的Wilson元收敛性分析

Abstract

Abstract:

In this paper, with the help of the wilson element, new semi-discrete and fullydiscrete schemes are proposed for parabolic integro-differential equation. Based on the properties of the element, through defining a new bilinear form, without using the technique of extrapolation and interpolated postprocessing, in the norm which is stronger than the usual H¹-norm, the convergence results with order O(h²)/O(h²+τ) for the primitive solution are obtained for the corresponding schemes, respectively. The above results are just one order higher than the usual error estimates for the wilson element. Here, h and τ are parameters of the subdivision in space and time step, respectively. Finally, numerical results are provided to confirm the theoretical analysis.

Key words: Parabolic integro-differential equation, Wilson element, Semi-discrete and fulldiscrete schemes, Convergence

CLC Number:

O242.21

Conggang Liang,Xiaoxia Yang,Dongyang Shi. Convergence Analysis of Wilson Element for Parabolic Integro-Differential Equation[J].Acta mathematica scientia,Series A, 2019, 39(5): 1158-1169.

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References 20

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$m\times m$	$\left\\| {u-u_h } \right\\|_h $	收敛阶	$\left\\| {u-u_h } \right\\|_0 $	收敛阶
$4\times 4$	0.023734626	---	0.000995509	---
$8\times 8$	0.006276340	1.9190	0.000187996	2.4047
$16\times 16$	0.001559389	2.0089	0.000043305	2.1181
$32\times 32$	0.000386405	2.0128	0.000010702	2.0167

$m\times m$	$\left\\| {u-u_h } \right\\|_h $	收敛阶	$\left\\| {u-u_h } \right\\|_0 $	收敛阶
$4\times 4$	0.039374206	---	0.001662729	---
$8\times 8$	0.010324365	1.9312	0.000341116	2.2852
$16\times 16$	0.002554045	2.0152	0.000082887	2.0410
$32\times 32$	0.000631856	2.0151	0.000020794	1.9950

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Convergence Analysis of Wilson Element for Parabolic Integro-Differential Equation

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