We analyze an immersed interface finite element method based on linear polynomials on noninterface triangular elements and piecewise linear polynomials on interface triangular elements. The flux jump condition is weakly enforced on the smooth interface. Optimal error estimates are derived in the broken H1-norm and L2-norm.

We show the multidimensional stability of subsonic phase transitions in a non-isothermal van der Waals fluid. Based on the existence result of planar waves in our previous work [1], a jump condition is posed on non-isothermal phase boundaries which makes the argument possible. Stability of planar waves both in one dimensional and multidimensional spaces are proved.

It presents and analyzes the Euler methods for stochastic age-dependent population equations driven by Poisson random jump measure; Under the Local Lipschitz condition, we prove that the Euler approximation solution converges to the exact solution in the mean-square sense. An example is given to illustrates our results.

This paper is concerned with the decentralized stabilization problem for a class of uncertain large-scale systems with Markovian jump parameters. The controllers use local subsystem states and neighboring mode information to generate local control inputs. A sufficient condition involving rank constrained linear matrix inequalities is proposed for the design of such controllers. A numerical exam...

We introduce the concepts of lumpability and commutativity of a continuous time discrete state space Markov process, and provide a necessary and sufficient condition for a lumpable Markov process to be commutative. Under suitable conditions we recover some of the basic quantities of the original Markov process from the jump chain of the lumped Markov process.

Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity. In this paper, we consider some type of game options and obtain explicit expressions through solving Stefanfree boundary problems under condition that the stock price is driven by some jump-diffusion process. Finally, we give a simple application about convertible bonds.

Purpose: Various kinematics and kinetics methods have been proposed for the assessment of jumping ability as a critical skill in professional volleyball players, but little is known about the accuracy and differences between these methods. Therefore, the objective of the current study was to answer the question “Is there any difference between the results of various kinetic methods in the asses...

Flood front is the jump interface where fluids distribute discontinuously, whose interface condition is the theoretical basis of a mathematical model of the multiphase flow in porous medium. The conventional interface condition at the jump interface is expressed as the continuous Darcy velocity and fluid pressure (named CVCM). Our study has inspected this conclusion. First, it is revealed that ...