Core Ideas The numerical solution of Richards' equation remains challenging. Space/time
discretization affects both computational effort and accuracy. Adaption of space and time …

In this paper, the Saul'yev finite difference scheme for a fully nonlinear partial differential
equation with initial and boundary conditions is analyzed. The main advantage of this …

Numerical modeling of water movement in both unsaturated soils and saturated
groundwater aquifers is important for water resource management simulations. The …

We study the unsaturated case of the Richards equation in three space dimensions with
Dirichlet boundary data. We first establish an a priori L∞-estimate. With its help, by means of …

Research on seepage flow in the vadose zone has largely been driven by engineering and
environmental problems affecting many fields of geotechnics, hydrology, and agricultural …

It is well established that damage to structures built on expansive soils is mainly caused by
changes in soil suction. Suction changes are generally attributed to changes in …

This work deals with the efficient numerical solution of nonlinear parabolic problems posed
on a two-dimensional domain Ω. We consider a suitable decomposition of domain Ω and we …

Fractional step Runge–Kutta methods are a class of additive Runge–Kutta schemes that
provide efficient time discretizations for evolutionary partial differential equations. This …

In this work, we present a cell-centered time-splitting technique for solving evolutionary
diffusion equations on triangular grids. To this end, we consider three variables (namely the …

For the heat equation on a rectangle and nonzero Dirichlet boundary conditions, we
consider an ADI orthogonal spline collocation method without perturbation terms, to specify …