This paper formulates and analyzes a weak solution to the coupling of time-dependent Navier-Stokes flow with Darcy flow under certain boundary conditions, one of them being the Beaver-Joseph-Saffman law on the interface. Existence and a priori estimates for the weak solution are shown under additional regularity assumptions. We introduce a fully discrete scheme with the unknowns being the Navie...

This is the first in a series of papers on implementing a discontinuous Galerkin method as a MATLAB /GNUOctave toolbox. The main goal is the development of techniques that deliver optimized computational performance combined with a compact, user-friendly interface. Our implementation relies on fully vectorized matrix / vector operations and is carefully documented; in addition, a direct mapping...

Abstract. Partitioned systems of ordinary differential equations are in qualitative terms characterized as monotonically max-norm stable if each sub-system is stable and if the couplings from one sub-system to the others are weak. Each sub-system of the partitioned system may be discretized independently by the backward Euler formula using solution values from the other sub-systems correspondin...

The exponential stability of continuous-time Hopfield neural networks is not preserved when implemented on digital computers by means of explicit numerical methods, whereas the implicit (or backward) Euler method preserves this exponential stability under exactly the same sufficient conditions as those previously obtained for the continuous model. The proof is based on the nonlinear measure app...

A multi-component reactive transport model, coupled to an existing thermal, hydraulic and mechanical model is investigated. The model is based on conservation of mass/energy principles for the flow and stress strain equilibrium for the mechanical behaviour. The resultant model is coupled to a geochemical model in order to capture geochemical interactions. Numerically, the Galerkin finite elemen...

In this work we are interested in the numerical approximation of 1D parabolic singularly perturbed problems of reaction–diffusion type. To approximate the multiscale solution of this problem we use a numerical scheme combining the classical backward Euler method and central differencing. The scheme is defined on some special meshes which are the tensor product of a uniform mesh in time and a sp...

The effect of formaldehyde on kinetics of biomass growth and consump­ tion of glucose by yeasts Candida tropicalis CC Y 29-7-33 has been inves­ tigated. For modelling of kinetics of biomass growth and consumption of the substrate the models according to Monod, Contois, and Andrews were applied. The parameters of kinetic equations were determined using the combined explicit and implicit Euler me...

We consider numerical approximation of solutions of singular second order differential equations. In particular, we study the backward (or implicit) Euler method. We prove results concerning consistency, global error and stability. We show that the global error is linear with respect to the step size. Numerical results are also given, which demonstrate the linear convergence and compare the num...

We propose a novel approach for the numerical integration of diffusion-type equations with variable and degenerate mobility or diffusion coefficient. Our focus is the Cahn-Hilliard equation which plays a prominent role in phase field models of fluids and soft materials but the methodology has a more general applicability. The central idea is a split method with a linearly implicit component and...

Partitioned systems of ordinary diierential equations are in qualitative terms characterized as monotonically max-norm stable if each subsystem is stable and if the couplings from one subsystem to the others are weak. Each subsystem of the partitioned system may be discretized independently by the backward Euler formula using solution values from the other subsystems corresponding to the previo...