On the temporal stability of least-squares methods for linear hyperbolic problems

被引:0
|
作者
Pacheco, Douglas R. Q. [1 ,2 ,3 ]
机构
[1] Rhein Westfal TH Aachen, Chair Computat Anal Tech Syst, Aachen, Germany
[2] Rhein Westfal TH Aachen, Chair Methods Model Based Dev Computat Engn, Aachen, Germany
[3] Norwegian Univ Sci & Technol, Dept Math Sci, Trondheim, Norway
关键词
Pure convection; Least-squares methods; Least-squares FEM; Unconditional stability; Numerical analysis; Advection-reaction equation; FINITE-ELEMENT METHODS; FORMULATIONS; FLOWS;
D O I
10.1016/j.camwa.2024.05.023
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Standard Galerkin methods often perform poorly for problems with low diffusion. In particular for purely convective transport, least -squares (LS) formulations provide a good alternative. While spatial stability is relatively straightforward in a least -squares finite element framework, estimates in time are restricted, in most cases, to one dimension. This article presents temporal stability proofs for the LS formulation of O -schemes, including unconditional stability for the backward Euler and Crank-Nicolson methods in two or three dimensions. The theory includes also the linear advection-reaction equation. A series of numerical experiments confirm that the new stability estimates are sharp.
引用
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页码:33 / 38
页数:6
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