数学季刊 >

2017 , Vol. 32 >Issue 2: 134 - 141

DOI: https://doi.org/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

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

收稿日期: 2016-10-23

  网络出版日期: 2020-10-23

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)；

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

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

Received date: 2016-10-23

  Online published: 2020-10-23

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)；

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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

本文引用格式

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

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

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