On Monotone Multigrid Methods for the Signorini Problem

Fast and Robust Numerical Solution of the Richards Equation in Homogeneous Soil

We derive and analyse a solver-friendly finite element discretization of a time discrete Richards equation based on Kirchhoff transformation. It can be interpreted as a classical finite element discretization in physical variables with non-standard quadrature points. Our approach allows for nonlinear outflow or seepage boundary conditions of Signorini type. We show convergence of the saturation...

Substructuring of a Signorini-type problem and Robin's method for the Richards equation in heterogeneous soil

We prove a substructuring result for a variational inequality concerning — but not restricted to — the Richards equation in homogeneous soil and including boundary conditions of Signorini’s type. This generalizes existing results for the linear case and leads to interface conditions known from linear variational equalities: continuity of Dirichlet and flux values in a weak sense. In case of the...

Adaptive Multigrid Methods for Signorini's Problem in Linear Elasti ity

Qualitative behaviour of solutions of Signorini problem with perturbing the unknown boundary : II. The multigrid method

Computational method for the Signorini problem in 2D is presented. Using qualitative properties of the solution on a perturbed boundary the iteration method for ®nding of the unknown boundary Cc is constructed. In the ®rst part of the method the boundary ac ˆ oCc is localized within two mesh points of a ®xed FE mesh. In the second part introducing the new multigrid algorithm the value ac is acc...

Unsaturated subsurface flow with surface water and nonlinear in - and outflow conditions ∗

We analytically and numerically analyze groundwater flow in a homogeneous soil described by the Richards equation, coupled to surface water represented by a set of ordinary differential equations (ODE’s) on parts of the domain boundary, and with nonlinear outflow conditions of Signorini’s type. The coupling of the partial differential equation (PDE) and the ODE’s is given by nonlinear Robin bou...