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个人信息Personal Information
副教授
硕士生导师
性别:男
毕业院校:大连理工大学
学位:博士
所在单位:数学科学学院
学科:计算数学
办公地点:创新园大厦A1025
联系方式:0411-84708351-8025
电子邮箱:zhangxp@dlut.edu.cn
Finding multiple solutions to elliptic systems with polynomial nonlinearity
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论文类型:期刊论文
发表时间:2021-01-10
发表刊物:NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
卷号:36
期号:5
页面范围:1074-1097
ISSN号:0749-159X
关键字:Bose-Einstein condensate; eigenfunction expansion discretization; error analysis; homotopy continuation; polynomial system; spurious solution; system of semilinear elliptic equations
摘要:Elliptic systems with polynomial nonlinearity usually possess multiple solutions. In order to find multiple solutions, such elliptic systems are discretized by eigenfunction expansion method (EEM). Error analysis of the discretization is presented, which is different from the error analysis of EEM for scalar elliptic equations in three aspects: first, the choice of framework for the nonlinear operator and the corresponding isomorphism of the linearized operator; second, the definition of an auxiliary problem in deriving the relation between the L-2 norm and H-1 norm of the Ritz projection error; third, the bilinearity/nonbilinearity of the linearized variational forms. The symmetric homotopy for the discretized equations preserves not only D-4 symmetry, but also structural symmetry. With the symmetric homotopy, a filter strategy and a finite element Newton refinement, multiple solutions to a system of semilinear elliptic equations arising from Bose-Einstein condensate are found.