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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 boundary conditions. This article provides two major new
contributions regarding these infiltration conditions. First, an existence
result for the continuous coupled problem is established with the help of a
regularization technique. Second, we analyze and validate a solver-friendly
discretization of the coupled problem based on an implicit-explicit time
discretization and on finite elements in space. The discretized PDE leads to
convex spatial minimization problems which can be solved efficiently by
monotone multigrid. Numerical experiments are provided using the DUNE numerics
framework.Comment: 34 pages, 5 figure
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