On the boundary element method for the Signorini problem of the Laplacian. (English) Zbl 0798.65106

For the Laplace equation with mixed boundary conditions of Signorini, Dirichlet and Neumann type two equivalent boundary variational inequalities are deduced. The second formulation, which is dual to the first, allows only Sigorini boundary conditions to be posed. Further, the discretization by a boundary element Galerkin method is described and quasi-optimal error estimates are given. The discretized problems are equivalent to quadratic optimization problems. A modified decomposition- coordination method is applied for its solution. Numerical examples confirm the predicted rate of convergence.
Reviewer: A.Pomp (Stuttgart)


65N38 Boundary element methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65K10 Numerical optimization and variational techniques
35J20 Variational methods for second-order elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
49J40 Variational inequalities
49M15 Newton-type methods
Full Text: DOI EuDML


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