An approach to the numerical verification of solutions for variational inequalities using Schauder fixed point theory

Boundary value problems

Cheon Seoung Ryoo¹ 

[1] Department of Mathematics, Hannam University, Daejeon, Korea

关键词: numerical verification;    error estimates;    variational inequalities;    unilateral boundary value problems for second order equations;    finite element method;    Schauder fixed point theory;   

DOI  :  10.1186/s13661-014-0235-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we describe a numerical method to verify the existence of solutions for a unilateral boundary value problems for second order equation governed by the variational inequalities. It is based on Nakao’s method by using finite element approximation and its explicit error estimates for the problem. Using the Riesz representation theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using Schauder fixed point theory, we construct a high efficiency numerical verification method that through numerical computation generates a bounded, closed, convex set which includes the approximate solution. Finally, a numerical example is illustrated. MSC: 65G20, 65G30, 65N15, 65N30.

【 授权许可】

CC BY