A technique for adaptive conjugate smoothing of discontinuous fields is presented in the paper. The described technique is applicable in various engineering problems and is especially effective when hybrid numerical – experimental methodologies are used. Adaptive image smoothing and stretching strategy is illustrated for a discontinuous plain stress field problem when photoelastic fringes repre...

The paper is devoted to the problems of an impulse control for the systems, whose dynamic is described by ordinary nonlinear differential equations. The problem of description for a discontinuous solution, arising from the using of an impulse control, is considered. The representation of the discontinuous (generalized) solutions is obtained on the basis of the method of a discontinuous time cha...

We prove the convergence of a discontinuous Galerkin method approximating the 2-D incompressible Euler equations with discontinuous initial vorticity: ω0 ∈ L2(Ω). Furthermore, when ω0 ∈ L∞(Ω), the whole sequence is shown to be strongly convergent. This is the first convergence result in numerical approximations of this general class of discontinuous flows. Some important flows such as vortex pa...

A theoretical framework for the analysis of discontinuous Galerkin approximations of the Maxwell eigenproblem with discontinuous coefficients is presented. Necessary and sufficient conditions for a spurious-free approximation are established, and it is shown that, at least on conformal meshes, basically all the discontinuous Galerkin methods in the literature actually fit into this framework. R...