where f ∈ L2(Ω). Let Th be a simplicial or convex quadrilateral triangulation of Ω. In C 0 interior penalty methods, we choose the discrete space Vh ⊂ H 1 0 (Ω) to be either a P` (` ≥ 2) triangular Lagrange finite element space or a Q` (` ≥ 2) tensor product finite element space associated with Th. By an integration by parts argument [4], it can be shown that the solution u of (1), which belong...

In this paper we present the continuous and discontinuous Galerkin methods in a unified setting for the numerical approximation of the transport dominated advection-reaction equation. Both methods are stabilized by the interior penalty method, more precisely by the jump of the gradient in the continuous case whereas in the discontinuous case the stabilization of the jump of the solution and opt...

We study stabilization methods for the discretization of convection-dominated elliptic convection-diffusion problems by linear finite elements. It turns out that there exist close relations between a new version of stabilization via local projection and the continuous interior penalty method. AMS Subject Classifications: 65 N15, 65N30, 65N12

This paper proposes a new method for real-time rigid body simulations based on a volumetric penalty method. The penalty method, which employs spring-damper model, is a simple and useful method for real-time simulation of multi-bodies. However, simple penalty method cannot handle face-face contact, because simple penalty method cannot find application point of reflection force. We suppose distri...

A family of problems for which the solution is a fixed size set is studied, using fitness functions with varying degrees of epistasis. An empirical comparison between a traditional crossover operator with a binary representation and a penalty function, and the representationindependent Random Assorting Recombination Operator (RAR) is performed. RAR is found to perform marginally better in all c...

If we believe that the two sequences x and y are similar then we might be able to optimally align them faster. For simplicity assume that m = n since our sequences are similar. If x and y align perfectly, then the optimal alignment corresponds to the diagonal in the dynamic programming table (now of size n × n). This is because all of the back pointers will be pointing diagonally. Therefore, if...

n this paper the problem of capacity planning under risk from demand and price/cost uncertainty of the finished products is addressed. The deterministic model is extended into a two-stage stochastic model with fixed recourse by means of various expected levels of demand as random. A recourse penalty is also included in the objective for both shortage and surplus in the finished products. The mo...

We propose a new approach to portfolio optimization under uncertainty in the assets’ return distribution. The main idea is to optimize penalty functionals which model the investor’s aversion against this uncertainty. We focus on two specific proposals with an important practical feature: the stability of the resulting portfolio composition under changing input variables. We review existing appr...

In this paper we describe two approaches to nonparametric regression. First, we consider the nearest neighbour approach, as a procedure which serves mainly for obtaining an ad hoc smoothing and interpolating. Next, we describe the roughness penalty approach. This gives a certain compromise between the demand for goodness-of-fit of regression curve to the given data and the condition that the re...

In this paper, we consider the ruin measures for two classes of risk processes. We assume that the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Historically, it has been assumed that the premium size is a constant. In this contribution, the premium income arrival process is a Poisson process. In this framework, both the integro-differential e...