间断Sobolev空间上一类反应扩散问题的新的变分形式

doi:10.13371/j.cnki.chin.q.j.m.2017.02.003

数学季刊 ›› 2017, Vol. 32 ›› Issue (2): 134-141.doi: 10.13371/j.cnki.chin.q.j.m.2017.02.003

间断Sobolev空间上一类反应扩散问题的新的变分形式

Institute of Applied Mathematics and School of Mathematics and Statistics, Henan University. College of Mathematics and Information Science, Henan University of Economics and Law

收稿日期:2016-10-23 出版日期:2017-06-30 发布日期:2020-10-23
作者简介:GE Zhi-hao(1980-), male, native of Huaiyang, Henan, an associate professor of Henan Uni- versity, Ph.D., engages in ¯nite element method for PDEs; CAO Ji-wei(1986-), male, native of Xiayi, Henan, a lecturer of Henan University of Economics and Law, Ph.D., engages in ¯nite element method and application.
基金资助:
Supported by the Natural Science Foundation of Henan Province(162300410031)； Supported by the Excellent Youth Program of the Basic Research Operating Expenses Program of Henan Province(yqpy20140039)；

A New Variational Formulation for a Kind of Reaction-diffusion Problem in Broken Sobolev Space

Institute of Applied Mathematics and School of Mathematics and Statistics, Henan University. College of Mathematics and Information Science, Henan University of Economics and Law

Received:2016-10-23 Online:2017-06-30 Published:2020-10-23
About author:GE Zhi-hao(1980-), male, native of Huaiyang, Henan, an associate professor of Henan Uni- versity, Ph.D., engages in ¯nite element method for PDEs; CAO Ji-wei(1986-), male, native of Xiayi, Henan, a lecturer of Henan University of Economics and Law, Ph.D., engages in ¯nite element method and application.
Supported by:
Supported by the Natural Science Foundation of Henan Province(162300410031)； Supported by the Excellent Youth Program of the Basic Research Operating Expenses Program of Henan Province(yqpy20140039)；

摘要/Abstract

摘要： In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalent to the standard Galerkin variational formulation. The method will be helpful to easily solve the original partial differential equation numerically. And the method is novel and interesting, which can be used to deal with some complicated problem, such as the low regularity problem, the differential-integral problem and so on.

关键词: broken Sobolev space, variational formulation, discontinuous Galerkin method, inf-sup condition

Abstract: In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalent to the standard Galerkin variational formulation. The method will be helpful to easily solve the original partial differential equation numerically. And the method is novel and interesting, which can be used to deal with some complicated problem, such as the low regularity problem, the differential-integral problem and so on.

Key words: broken Sobolev space, variational formulation, discontinuous Galerkin method; inf-sup condition

中图分类号:

O177

葛志昊, 曹济伟. 间断Sobolev空间上一类反应扩散问题的新的变分形式[J]. 数学季刊, 2017, 32(2): 134-141.

GE Zhi-hao, CAO Ji-wei. A New Variational Formulation for a Kind of Reaction-diffusion Problem in Broken Sobolev Space[J]. Chinese Quarterly Journal of Mathematics, 2017, 32(2): 134-141.

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间断Sobolev空间上一类反应扩散问题的新的变分形式

A New Variational Formulation for a Kind of Reaction-diffusion Problem in Broken Sobolev Space

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