12 citations · 25 across the 3 of their papers we have counts for
6 papers
Stabilizing Radial Basis Function Methods for Conservation Laws Using Weakly Enforced Boundary Conditions
Jan Glaubitz, Anne Gelb
It is well understood that boundary conditions (BCs) may cause global radial basis function (RBF) methods to become unstable for hyperbolic conservation laws (CLs). Here we investi…
Towards Stable Radial Basis Function Methods for Linear Advection Problems
Jan Glaubitz, Elise Le Mélédo, Philipp Öffner
In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced stro…
Constructing Positive Interpolatory Cubature Formulas
Jan Glaubitz
Positive interpolatory cubature formulas (CFs) are constructed for quite general integration domains and weight functions. These CFs are exact for general vector spaces of continuo…
Stable High Order Quadrature Rules for Scattered Data and General Weight Functions
Jan Glaubitz
Numerical integration is encountered in all fields of numerical analysis and the engineering sciences. By now, various efficient and accurate quadrature rules are known; for instan…
Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points
Jan Glaubitz, Philipp Oeffner
In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We…
Shock Capturing by Bernstein Polynomials for Scalar Conservation Laws
Jan Glaubitz
A main disadvantage of many high-order methods for hyperbolic conservation laws lies in the famous Gibbs-Wilbraham phenomenon, once discontinuities appear in the solution. Due to t…