In this paper, a weak formulation of the discontinuous variable coefficient Poisson equation with interfacial jumps is studied. The existence, uniqueness and regularity of solutions of this problem are obtained. It is shown that the application of the Ghost Fluid Method by Fedkiw, Kang, and Liu to this problem in [9] can be obtained in a natural way through discretization of the weak formulatio...

The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Although the finite element method (FEM) is a well-established method for modeling nonlinear problems, it often encounters difficulties for large deformation analyses due to the mesh distortion issues. Because no mesh is used, the meshless methods show very good potential for the la...

in this paper we consider the european continuous installment call option. then  its linear complementarity formulation is given. writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. finally finite element method is applied to price the european continuous installment call option.

Abstract. The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005. The recovery method approximates the solution of the diffusion equation in a discontinuous function space, while inter-element coupling is achieved by a local L2 projection that recovers a smooth continuous function underlying the dis...

A meshless approximation and local integral equation (LIE) formulation are proposed for elastodynamic analysis of a hollow cylinder made of quasicrystal materials with decagonal quasicrystal properties. The cylinder is assumed to be under shock loading. Therefore, the general transient elastodynamic problem is considered for coupled phonon and phason displacements and stresses. The equations of...

We provide sufficient optimality conditions for optimal control problems with bang-bang controls. Building on a structural assumption on the adjoint state, we additionally need a weak second-order condition. This second-order condition is formulated with functions from an extended critical cone, and it is equivalent to a formulation posed on measures supported on the set where the adjoint state...

A space-time discontinuous Galerkin finite element method for the compressible Navier-Stokes equations is presented. We explain the space-time setting, derive the weak formulation and discuss our choices for the numerical fluxes. The resulting numerical method allows local grid adaptation as well as moving and deforming boundaries, which we illustrate by computing the flow around a 3D delta win...

We prove the regularity of weak 1/2−harmonic maps from the real line into a sphere. The key point in our result is first a formulation of the 1/2−harmonic map equation in the form of a non-local linear Schrödinger type equation with a 3-terms commutators in the right-hand-side . We then establish a sharp estimate for these 3-commutators.

In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld's radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in eithe...