We describe a strategy for detecting discontinuities and for limiting spurious oscillations near such discontinuities when solving hyperbolic systems of conservation laws by high-order discontinuous Galerkin methods. The approach is based on a strong superconvergence at the outflow boundary of each element in smooth regions of the flow. By detecting discontinuities in such variables as density ...

The realization of phase discontinuities across metasurfaces has led to a new class of reflection and refraction. Here we present theory and experiment on the discontinuous propagation of wavepackets across subwavelength-thickness meta-atoms. Using acoustic waves, we observe the process of wavepackets traversing a meta-atom with abrupt displacements, which appear as path discontinuities on a sp...

In computer-aided design and meshing, it is often important to identify the discontinuities (singularities) in coarse surface meshes. Due to the potential low resolution and noise, it is challenging to detect such features. We propose systematic characterizations of the edges, corners, and curves at the singularities of a mesh and develop algorithms to identify these geometric features. Our alg...

In the Fourier series approximation of real functions discontinuities of the functions or their derivatives cause problems like Gibbs phenomenon or slow uniform convergence. In the case of a nite number of isolated discontinuities the problems can be to a large extend recti ed by using periodic splines in the series. This modi ed Fourier series (Spline-Fourier series) is applied to the numerica...

When using high-order accurate shock-capturing methods, e.g., weighted essentially non-oscillatory schemes (WENO), numerical errors are often generated in simulations of isolated contact discontinuities and material interfaces when trying to capture these features on a grid. Spurious pressure oscillations are generated at interfaces and contacts propagate through the flow field. In addition, te...

The paper presents the major principles and concepts of a dependency grammar theory of discontinuities for English and German (and presumably for many other languages as well). Discontinuities are identified in terms of traditional projectivity violations. These violations are then reanalyzed according to the Rising Principle. This principle sees the relevant constituent attaching to a word tha...