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

页码：1365 / 1385

页数：21

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