An iterative algorithm based on the piecewise linear system for solving bilateral obstacle problems

Abstract

In this paper, we derive the piecewise linear system (PLS) associated with the bilateral obstacle problem and illustrate the equivalence between the linear system and finite-dimensional complementary problem. The existence and the uniqueness of the solution to the PLS are also demonstrated. Based on the PLS, a Picard iterative algorithm is proposed. The convergence analysis is given and examples are presented to verify the effectiveness of the method.

Analysis of a new kind of elastic-rigid bilateral obstacle problem

“…The classical bilateral obstacle problem can be described as follows: assume that the elastic membrane (1) is a homogeneous membrane occupying a domain Ω ; (2) lies between a lower obstacle of height ϕ and a upper obstacle of height ψ ; (3) is equally stretched in all directions by a uniform tension and loaded by a normal uniformly distributed force f [16]. Let u be the vertical displacement component of the membrane.…”

“…In the past decades, mathematical theories and numerical analysis of this model have been established extensively and thoroughly. For more details, we recommend the works by Ran and Cheng [1], Bouchlaghem and Mermri [2,3], Duvaut and Lions [4], Hoppe [5], Imoro [6], Kärkkäinen [7], Kinderlehrer and Stampacchia [8], Kornhuber [9,10], Murea and Tiba [11,12], Ran et al [13], Rodrigues [14], Tarvainen [15], and Yuan and Cheng [16].…”

“…For more details, we refer to the works by Ran et al [13] , Yuan and Cheng [16], and Glowinski [19].…”