We investigate the discretization of optimal boundary control problems for elliptic equations by the boundary concentrated finite element method. We prove that the discretization error ‖u−uh‖L2(Γ) decreases like N−1, where N is the total number of unknowns. This makes the proposed method favorable in comparison to the h-version of the finite element method, where the discretization error behave...

In this paper we target at developing discretization-invariant, namely dimension-independent, Markov chain Monte Carlo (MCMC) methods to explore PDEconstrained Bayesian inverse problems in infinite dimensional parameter spaces. In particular, we present two frameworks to achieve this goal: Metropolize-then-discretize and discretize-then-Metropolize. The former refers to the method of first prop...

‎In the present paper‎, ‎optimal heating of temperature field which is modelled as a boundary optimal control problem‎, ‎is investigated in the uncertain environments and then it is solved numerically‎. ‎In physical modelling‎, ‎a partial differential equation with stochastic input and stochastic parameter are applied as the constraint of the optimal control problem‎. ‎Controls are implemented ...

In this paper we deal with a numerical solution of the compressible Navier-Stokes equations with the aid of higher order schemes. We use the discontinuous Galerkin finite element method for the space semi-discretization and a backward difference formula for the time discretization. Moreover, a linearization of inviscid/viscous fluxes and a suitable explicit extrapolation for nonlinear terms lea...

We investigate the discretization of optimal boundary control problems for elliptic equations by the boundary concentrated finite element method. We prove that the discretization error ‖u∗−u∗h‖L2(Γ) decreases like N , where N is the total number of unknowns. This makes the proposed method favorable in comparison to the h-version of the finite element method, where the discretization error behav...

In this paper, space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convectionreaction equation without control constraints is studied. Time discretization is performed by discontinuous Galerkin method with piecewise constant and linear polynomials, while symmetric interior penalty Galerkin with upwinding is used for spa...

In this paper we consider a backward parabolic partial differential equation, called the Black-Scholes equation, governing American and European option pricing. We present a numerical method combining the Crank-Nicolson method in the time discretization with a hybrid finite difference scheme on a piecewise uniform mesh in the spatial discretization. The difference scheme is stable for the arbit...

For lamellar gratings and other layered periodic structures, the modal methods (including both analytic and numerical ones) are often the most efficient, since they avoid the discretization of one spatial variable. The pseudospectral modal method (PSMM) previously developed for in-plane diffraction problems of one-dimensional gratings achieves high accuracy for a small number of discretization ...

Abstract. Differential algebraic equations have wide applications in the field of engineering and science where the mathematical models form the descriptor systems. Analysis and modeling of the solutions of such systems need to handle with the different equations related to the systems. A time-domain discretization, for example, finite difference, finite volume, etc., may lead to DAEs of descri...

In this paper, a general framework for the analysis of multigrid methods for mortar finite elements is considered. The numerical realization is based on the algebraic saddle point formulation arising from the discretization of second order elliptic equations on nonmatching grids. Suitable discrete Lagrange multipliers on the interface guarantee weak continuity and an optimal discretization sche...