We consider two-dimensional elliptic problems with discontinuous coefficients discretized by the finite element method on geometrically conforming nonmatching triangulations across the interface using the mortar technique. The resulting discrete problem is solved by a dual-primal FETI method. In this paper we introduce and analyze a preconditioner with a special scaling of coefficients and step...

Knowledge of a truncated Fourier series expansion for a discontinuous 2^-periodic function, or a truncated Chebyshev series expansion for a discontinuous nonperiodic function defined on the interval [-1, 1], is used in this paper to accurately and efficiently reconstruct the corresponding discontinuous function. First an algebraic equation of degree M for the M locations of discontinuities in e...

this paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. the method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions.the construction of the nonstandard method is based on the special treatment of the interface using suitable jump condition...

We prove a maximum principle for linear second order elliptic systems in divergence form with discontinuous coefficients under a suitable condition on the dispersion of the eigenvalues of the coefficients matrix.

The Dirichlet problem for non-divergence parabolic equations with discontinuous in time coefficients.