Paper Info
Title
The lumped mass finite element method for surface parabolic problems: Error estimates and maximum principle.
Abstract
The lumped mass method is extended to the surface finite element method for solving the surface parabolic equations. The main purpose of the proposed method is to overcome the difficulty that the surface finite element method does not guarantee the maximal principle of the surface heat equation. Optimal error estimates are given for the semi-discrete and fully-discrete schemes of the proposed method respectively. The maximum principle is shown for surface heat equations and its preservation by the lumped mass surface finite element under the Delaunay type triangulation. Moreover, some results of positivity and monotonicity are derived for nonlinear parabolic equations. Finally some numerical experiments are displayed to illustrate the validity and numerical performance of the proposed method.
Year
DOI
Venue
2018
10.1016/j.camwa.2018.04.031
Computers & Mathematics with Applications
Keywords
Field
DocType
Surface parabolic equation,Surface finite element method,Lumped mass method,Maximum principle,Error estimates
Parabolic partial differential equation,Monotonic function,Maximum principle,Mathematical analysis,Finite element method,Triangulation (social science),Heat equation,Mathematics,Parabola,Delaunay triangulation
Journal
Volume
Issue
ISSN
76
3
0898-1221
Citations 
PageRank 
References 
0
0.34
6
Authors
3
Name
Order
Citations
PageRank
Xufeng Xiao112.38
Xinlong Feng213522.33
Jin Yun Yuan35210.57