This paper proposes a mortar finite element method for solving the two-dimensional second-order elliptic problem with jumps in coefficients across the interface between two subregions. Non-matching finite element grids are allowed on the interface, so independent triangulations can be used in different subregions. Explicitly realizable mortar conditions are introduced to couple the individual d...

In this paper, we use the Yoshida approximation to prove the existence and uniqueness of a solution for the backward doubly stochastic differential equation when the generator is monotone and continuous. Before that we present the results for existence and uniqueness of an adapted solution of the backward doubly stochastic differential equation under some generals conditions.

in this paper, the linearly conforming enriched radial basis point interpolation method is implemented for the elasto-plastic analysis of discontinuous medium. the linear conformability of the method is satisfied by the application of stabilized nodal integration and the enrichment of radial basis functions is achieved by the addition of linear polynomial terms. to implement the method for the ...

We propose several formulations for recovering discontinuous coefficients in elliptic problems by using total variation (TV) regularization. The motivation for using TV is its wellestablished ability to recover sharp discontinuities. We employ an augmented Lagrangian variational formulation for solving the output-least-squares inverse problem. In addition to the basic outputleast-squares formul...

A second-order difference scheme for a first-order elliptic system with discontinuous coefficients is derived and studied. This approximation can be viewed as an improvement of the well-known scheme with harmonic averaging of the coefficients for a second order elliptic equation, which is first-order accurate for the gradient of the solution. The numerical experiments confirm the second order c...

We will show that the same type of estimates known for the fundamental solutions for scalar parabolic equations with smooth enough coefficients hold for the first order derivatives of fundamental solution with respect to space variables of scalar parabolic equations of divergence form with discontinuous coefficients. The estimate is very important for many applications. For example, it is impor...

Second order elliptic problems with discontinuous coefficients are considered. The problem is discretized by the finite element method on geometrically conforming non-matching triangulations across the interface using the mortar technique. The resulting discrete problem is solved by a FETI-DP method. We prove that the method is convergent and its rate of convergence is almost optimal and indepe...

Recent work shows that the block-parallel CARP-CG algorithm [Parallel Computing 36, 2010] is extremely effective on sparse nonsymmetric linear systems with very small diagonal elements, including cases with discontinuous coefficients. In contrast to most known solvers, the effectiveness of CARP-CG often improves as the diagonal elements become smaller. This property is shown to follow from the ...

A second order elliptic problem with highly discontinuous coefficients has been considered. The problem is discretized by two methods: 1) continuous finite element method (FEM) and 2) composite discretization given by a continuous FEM inside the substructures and a discontinuous Galerkin method (DG) across the boundaries of these substructures. The main goal of this paper is to design and analy...

We propose and analyze a C spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise constant coefficients case and verified by numerical tests. Furthermore, the asymptotical equivalence between a Gauss-Lobatto collocation method and a spectral Galerkin method is establ...