Error estimates for an approximation of a problem of percolation in gently sloping beaches (Q1820559)

The authors consider the problem of finding error estimates for the linear finite element approximate solution of a parabolic variational inequality. This variational inequality is related to a free boundary value problem arising from a model of water percolation in nearly horizontal sand-banks in the intertidal zone. Under suitable regularity assumptions on the given data, the error estimates are derived by using piecewise linear finite element discretization in space and backward finite differences in time. In particular, for the choice, \(\Delta t=Ch^{3/2}\), the error estimate leads to a \(O(h^{3/2})\) rate of convergence.