Linear systems with large differences between coefficients (“discontinuous coefficients”) arise in many cases in which partial differential equations (PDEs) model physical phenomena involving heterogeneous media. The standard approach to solving such problems is to use domain decomposition (DD) techniques, with domain boundaries conforming to the boundaries between the different media. This app...

We propose an extension of the discontinuous Galerkin local orthogonal decomposition multiscale method, presented in [14], to convection-diffusion problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the discontinuous Galerkin method allows us to better cope with multiscale features as well as interior/boundary layers in the solution. ...

This paper is concerned with a weakly coupled system of quasilinear parabolic equations where the coefficients are allowed to be discontinuous and the reaction functions may depend on continuous delays. By the method of upper and lower solutions and the associated monotone iterations and by difference ratios method and various estimates, we obtained the existence and uniqueness of the global pi...

A new multigrid algorithm is constructed for the solution of linear systems of equations which arise from the discretization of elliptic PDEs. It is defined in terms of the difference scheme on the fine grid only, and no rediscretization of the PDE is required. Numerical experiments show that this algorithm gives high convergence rates for several classes ofproblems: symmetric, nonsymmetdc and ...

The coupling of cell-centered finite volume method with primal discontinuous Galerkin method is introduced in this paper for elliptic problems. Convergence of the method with respect to the mesh size is proved. Numerical examples confirm the theoretical rates of convergence. Advantages of the coupled scheme are shown for problems with discontinuous coefficients or anisotropic diffusion matrix.

This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete l...

In this second part of paper the description of conservative averaging method for partial differential (or integro-differential) equation with discontinuous coefficients in cylinder type domain is given. The conservative averaging is carried out in two orthogonal directions. Different types of boundary conditions are examined. Key-Words: partial differential equations, discontinuous coefficient...

We propose an extension of the discontinuous Galerkin multiscale method, presented in [11], to convection dominated problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the discontinuous Galerkin method allows us to better cope with multiscale features as well as boundary layers in the solution. In the proposed method the trail and tes...

The existence theory for the vector valued stochastic differential equations under G-Brownian motion (G-SDEs) of the type Xt = X0 + ∫ t 0 f (v,Xv)dv+ ∫ t 0 g(v,Xv)d〈B〉v + ∫ t 0 h(v,Xv)dBv, t ∈ [0,T ], with first two discontinuous coefficients is established. It is shown that the G-SDEs have more than one solution if the coefficient g or the coefficients f and g simultaneously, are discontinuous...

We use the concept of the Filippov solution to study the dynamics of a class of delayed dynamical systems with discontinuous right-hand side, which contains the widely studied delayed neural network models with almost periodic self-inhibitions, interconnection weights, and external inputs. We prove that diagonal-dominant conditions can guarantee the existence and uniqueness of an almost periodi...