Adaptive finite element method for parabolic equations with Dirac measure

被引:6
作者
Gong, Wei [1 ]
Liu, Huipo [2 ]
Yan, Ningning [3 ]
机构
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China
[2] Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China
[3] Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, NCMIS,LSEC, Beijing 100190, Peoples R China
基金
中国国家自然科学基金;
关键词
Parabolic equation; Dirac measure; Adaptive finite element method; Space-time discretization; A posteriori error estimates; POINTWISE STATE CONSTRAINTS; APPROXIMATION; ALGORITHM; TIME;
D O I
10.1016/j.cma.2017.08.051
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper we study the adaptive finite element method for parabolic equations with Dirac measure. Two kinds of problems with separate measure data in time and measure data in space are considered. It is well known that the solutions of such kind of problems may exhibit lower regularity due to the existence of the Dirac measure, and thus fit to adaptive FEM for space discretization and variable time steps for time discretization. For both cases we use piecewise linear and continuous finite elements for the space discretization and backward Euler scheme, or equivalently piecewise constant discontinuous Galerkin method, for the time discretization, the a posteriori error estimates based on energy and L-2 norms for the fully discrete problems are then derived to guide the adaptive procedure. Numerical results are provided at the end of the paper to support our theoretical findings. (C) 2017 Elsevier B.V. All rights reserved.
引用
收藏
页码:217 / 241
页数:25
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