A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate i...

This paper presents a numerical model based on one-dimensional Beji and Nadaoka's Extended Boussinesq equations for simulation of periodic wave shoaling and its decomposition over morphological beaches. A unique Galerkin finite element and Adams-Bashforth-Moulton predictor-corrector methods are employed for spatial and temporal discretization, respectively. For direct application of linear fini...

We consider PDE constrained shape optimization in the framework of finite element discretization of the underlying boundary value problem. Our approach employs (i) B-spline based representations of the deformation diffeomorphism, and (ii) superconvergent domain integral expressions for the shape gradient. We study the balance of the discretization errors of the finite element method and the B-s...

This paper deals with the full discretization of quasistatic 3D Signorini problems with local Coulomb friction and a coefficient of friction which may depend on the solution. After a time discretization we obtain a system of static contact problems with Coulomb friction. Each of these problems is solved by the T-FETI domain decomposition method used in auxiliary contact problems with Tresca fri...

In this work we consider a parabolic system of two linear singularly perturbed equations of reaction-diffusion type coupled in the reaction terms. The small values of the diffusion parameters, in general, cause that the solution has boundary layers at the ends of the spatial domain. To obtain an efficient approximation of the solution we propose a numerical method combining the Crank-Nicolson m...

The standard methodology handling nonlinear PDE’s involves the two steps: numerical discretization to get a set of nonlinear algebraic equations, and then the application of the Newton iterative linearization technique or its variants to solve the nonlinear algebraic systems. Here we present an alternative strategy called direct linearization method (DLM). The DLM discretization algebraic equat...

Subfilter scalar variance is a critical indicator of small scale mixing in large eddy simulation LES of turbulent combustion and is an important parameter of conserved scalar based combustion models. Realistic combustion models have a highly nonlinear dependence on the conserved scalar, making the prediction of flow thermochemistry sensitive to errors in subfilter variance modeling, including e...

We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. With an H(Ω) regular elliptic PDE on two-dimensional domains as constraint, we prove that the discretization error ‖u∗ − uh‖L2(Γ) decreases like N −δ, where N denotes the total number of unknowns. For the case δ = 1 in convex polygonal domains, t...

In this paper we develop two novel numerical methods for the partial integral differential equation arising from the valuation of an option whose underlying asset is governed by a jump diffusion process. These methods are based on a fitted finite volume method for the spatial discretization, an implicit-explicit time stepping scheme and the Crank-Nicolson time stepping method. We show that the ...

The variable order wave equation plays a major role in acoustics, electromagnetics, and fluid dynamics. In this paper, we consider the space-time variable order fractional wave equation with variable coefficients. We propose an effective numerical method for solving the aforementioned problem in a bounded domain. The shifted Jacobi polynomials are used as basis functions, and the variable-order...