notesum.ai

Published at November 26

A weighted scalar auxiliary variable method for solving gradient flows: bridging the nonlinear energy-based and Lagrange multiplier approaches

math.NA

cs.NA

physics.comp-ph

65M22, 65M70, 35K35, 35K55

Released Date: November 26, 2024

Authors: Qiong-Ao Huang, Wei Jiang, Jerry Zhijian Yang, Cheng Yuan

Arxiv: http://arxiv.org/abs/2411.17403v1

Refer to caption

$\tau$		$\\|\phi_{\tau}-\phi_{\tau/2}\\|_{2}$	Rate		$\\|\phi_{\tau}-\phi_{\tau/2}\\|_{\infty}$	Rate		$\\|\phi_{\tau}-\phi_{\tau/2}\\|_{2}$	Rate		$\\|\phi_{\tau}-\phi_{\tau/2}\\|_{\infty}$	Rate
		$\lambda=0.5$						$\lambda=\lambda_{\min}$
$0.5^{2}\times 10^{-3}$		1.5943e-4			7.0923e-5			1.5906e-4			7.0719e-5
$0.5^{3}\times 10^{-3}$		4.1174e-5	1.9531		1.8313e-5	1.9534		4.0986e-5	1.9563		1.8209e-5	1.9575
$0.5^{4}\times 10^{-3}$		1.0455e-5	1.9775		4.6498e-6	1.9776		1.0361e-5	1.9840		4.5972e-6	1.9858
$0.5^{5}\times 10^{-3}$		2.6338e-6	1.9890		1.1711e-6	1.9893		2.5865e-6	2.0021		1.1447e-6	2.0058
$0.5^{6}\times 10^{-3}$		6.6070e-7	1.9951		2.9351e-7	1.9965		6.3717e-7	2.0212		2.8027e-7	2.0301
$0.5^{7}\times 10^{-3}$		1.6511e-7	2.0005		7.2839e-8	2.0106		1.5349e-7	2.0536		6.6150e-8	2.0830