In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with the linearized semi-implicit Euler scheme for the equations of incompressible miscible flow in porous media. We prove that the optimal L2 error estimates hold without any time-step (convergence) conditions, while all previous works require certain time-step restrictions. Our theoretical result...

This paper studies the mean stability of positive semi-Markovian jump linear systems. We show that their mean stability is characterized by the spectral radius of a matrix that is easy to compute. In deriving the condition we use a certain discretization of a semi-Markovian jump linear system that preserves stability. Also we show a characterization for the exponential mean stability of continu...

Generalized semi-infinite optimization problems (GSIP) are considered. It is investigated how the numerical methods for standard semi-infinite programming (SIP) can be extended to GSIP. Newton methods can be extended immediately. For discretization methods the situation is more complicated. These difficulties are discussed and convergence results for a discretizationand an exchange method are d...

Based on a simple stability analysis for the semi{implicit Euler discretization a new dynamic sparsing procedure is derived. This procedure automatically eliminates \small" elements of the Jacobian matrix. As a consequence, the amount of work needed to handle the linear algebra within a semi{implicit extrapolation integrator can be reduced drastically. Within the course of integration the spars...

We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak solutions to the semi-discretization of the problem as well as convergence of the approximating sequences. The semi-discretization shows that facets must form. For ...

We present an easy to implement drift splitting numerical method for the approximation of stiff, nonlinear stochastic differential equations (SDEs). The method is an adaptation of the semi-implicit backward differential formula (SBDF) multistep method for deterministic differential equations and allows for a semi-implicit discretization of the drift term to remove high order stability constrain...