We investigate smooth and sparse optimal control problems for convective FitzHughNagumo equation with travelling wave solutions in moving excitable media. The cost function includes distributed space-time and terminal observations or targets. The state and adjoint equations are discretized in space by symmetric interior point Galerkin (SIPG) method and by backward Euler method in time. Several ...

We de8ne a time-stepping procedure to integrate the equations of motion of sti+ multibody dynamics with contact and friction. The friction and non-interpenetration constraints are modelled by complemen9 tarity equations. Sti+ness is accommodated by a technique motivated by a linearly implicit Euler method. We show that the main subproblem, a linear complementarity problem, is consistent for a s...

This paper proposes and analyzes two fully discrete mixed interior penalty discontinuous Galerkin (DG) methods for the fourth order nonlinear Cahn-Hilliard equation. Both methods use the backward Euler method for time discretization and interior penalty discontinuous Galerkin methods for spatial discretization. They differ from each other on how the nonlinear term is treated, one of them is bas...

Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-steppingmethod to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods ...

In this paper we consider a meshfree radial basis function approach for the valuation of pricing options with non-smooth payoffs. By taking advantage of parallel architecture, a strongly stable and highly accurate time stepping method is developed with computational complexity comparable to the implicit Euler method implemented concurrently on each processor. This, in collusion with the radial ...

The inhomogeneous Poisson (Laplace) equation with internal Dirichlet boundary conditions has recently appeared in several applications ranging from image segmentation [1–3] to image colorization [4], digital photo matting [5, 6] and image filtering [7, 8]. In addition, the problem we address may also be considered as the generalized eigenvector problem associated with Normalized Cuts [9], the l...

We propose a numerical approximation method for the Cahn-Hilliard equations that incorporates continuous data assimilation in order to achieve long time accuracy. The uses C0 interior penalty spatial discretization of fourth equations, together with backward Euler temporal discretization. prove is stable and accurate, arbitrarily inaccurate initial conditions, provided enough measurements are i...

In this work we consider a mathematical model for two-phase flow in porous media.The fluids are assumed immiscible and incompressible and the solid matrix non-deformable. The mathematical model for the two-phase flow is written in terms of the global pressure and a complementary pressure (obtained by using the Kirchhoff transformation) as primary unknowns. For the spatial discretization, finite...

This paper deals with a method for the numerical solution of parabolic initialboundary value problems in two-dimensional polygonal domains Ω which are allowed to be non-convex. The Nitsche finite element method (as a mortar method) is applied for the discretization in space, i.e. non-matching meshes are used. For the discretization in time, the backward Euler method is employed. The rate of con...

Abstract. An adaptive algorithm, based on residual type a posteriori indicators of errors measured in L∞(L2) and L2(L2) norms, for a numerical scheme consisting of implicit Euler method in time and discontinuous Galerkin method in space for linear parabolic fourth order problems is presented. The a posteriori analysis is performed for convex domains in two and three space dimensions for local s...