Backward difference time discretization of parabolic differential equations on evolving surfaces

被引：63
|
作者：
Lubich, Christian [1 ]
Mansour, Dhia [1 ]
Venkataraman, Chandrasekhar [2 ]
机构：
[1] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany
[2] Univ Sussex, Dept Math, Falmer BN1 9QH, England
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2013年 / 33卷 / 04期
基金：
英国工程与自然科学研究理事会;
关键词：
parabolic PDE; evolving-surface finite element method; backward difference formula; G-stability; multiplier technique; energy estimates;
D O I：
10.1093/imanum/drs044
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A linear parabolic differential equation on a moving surface is discretized in space by evolving-surface finite elements and in time by backward difference formulas (BDFs). Using results from Dahlquist's G-stability theory and Nevanlinna & Odeh's multiplier technique together with properties of the spatial semidiscretization, stability of the full discretization is proved for BDF methods up to order 5 and optimal-order convergence is shown. Numerical experiments illustrate the behaviour of the fully discrete method.
引用
收藏
页码：1365 / 1385
页数：21
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