Resolvent conditions for discretizations of diffusion-convection-reaction equations in several space dimensions Original Research Article

Resolvent conditions are useful in the stability analysis of numerical methods for the solution of linear initial value problems. Under such conditions one can prove stability estimates in terms of the number of time steps n and the dimension s of the space. This paper addresses the question of whether those resolvent conditions are fulfilled if the linear initial value problems under consideration arise from the semi-discretization of a diffusion-convection-reaction equation in several space dimensions. In this paper some relevant results from the literature are reviewed, some of these results are extended, and some new results are proved.