Stability and continuation of solutions to obstacle problems
The paper is concerned with obstacle problems in elasticity, formulated in terms of variational inequalities. Main topics are criteria for stable solutions (strict local minima of a related energy functional), and the problem of numerical continuation of solutions either with respect to a norm or with respect to an eigenvalue parameter. Theoretical results recently obtained by the authors are summarized and applied to obstacle problems for beams and plates [e.g.: J. Comput. Appl. Math. 26, No.1/2, 23-34 (1989; Zbl 0672.65040); Math. Methods Appl. Sci. 11, No.1, 95-104 (1989; Zbl 0669.65053); 9, 240-250 (1987; Zbl 0627.73052); 8, 516-532 (1986; Zbl 0613.73046)]. In particular, a survey of numerical methods is given which have been used to compute stability bounds.
closed convex subset of real Hilbert space
nonlinearity of space of admissible vectors
optimal regularity properties of solutions
scientific article; zbMATH DE number 4209763
scientific article