We present upper-semicontinuity results for attractors and the chain-recurrent set of differential inclusions, in particular w.r.t. discretizations, and applications to game dynamics.

In this paper, we consider a discrete delay problem with negative feedback _ x(t) = f(x(t); x(t?1)) along with a certain family of time discretizations with stepsize 1=n. In the original problem, the attractor admits a Morse decomposition. We proved in G,H] that the discretized problems have global attractors. It was proved in G,M] that such attractors also admit Morse decompositions. In G,H] w...

We present an accurate and efficient discretization approach for the adaptive discretization of typical model equations employed in numerical weather prediction. A semi-Lagrangian approach is combined with the TR-BDF2 semi-implicit time discretization method and with a spatial discretization based on adaptive discontinuous finite elements. The resulting method has full second order accuracy in ...

Numerical solution for ordinary di erential equations (ODEs) is an established research area. There are many well established methods, such as Runge-Kutta methods and multi-step methods, for such purposes. There are also many excellent books on this subject, for example [1], [13] and [17]. Special purpose ODE solvers, such as those for sti ODEs, are also well studied. See, e.g., [6]. However, t...

It is well-known that the performance of POD and POD-DEIM methods depends on the selection of the snapshot locations. In this work, we consider the selections of the locations for POD and POD-DEIM snapshots for spatially semi-discretized linear or semi-linear parabolic PDEs. We present an approach that for a fixed number of snapshots the optimal locations may be selected such that the global di...

In this paper a nonlinear penalty method via a nonlinear Lagrangian function is introduced for semi-infinite programs. A convergence result is established which shows that the sequence of optimal values of nonlinear penalty problems converges to that of semi-infinite programs. Moreover a conceptual convergence result of a discretization method with an adaptive scheme for solving semi-infinite p...

Most often, in the discretization of a partial differential equation, one or several intermediate non-discrete problems appear between the continuous and discrete ones. In this case, the discretization is called multi-step. Let us quote timedependent equations where the intermediate problem is the time semi-discrete problem and the equations where a stabilization term is added befor the discret...

Based on the authors' previous work which established theoretical foundations of two, conceptual, successive convex relaxation methods, i.e., the SSDP (Successive Semide nite Programming) Relaxation Method and the SSILP (Successive Semi-In nite Linear Programming) Relaxation Method, this paper proposes their implementable variants for general quadratic optimization problems. These problems have...

Based on the authors' previous work which established theoretical foundations of two, conceptual, successive convex relaxation methods, i.e., the SSDP (Successive Semide nite Programming) Relaxation Method and the SSILP (Successive Semi-In nite Linear Programming) Relaxation Method, this paper proposes their implementable variants for general quadratic optimization problems. These problems have...