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5 papers · 2 filters
Double-grid quadrature with interpolation-projection (DoGIP) as a novel discretisation approach: An application to FEM on simplexes
Jaroslav Vondřejc
This paper is focused on the double-grid integration with interpolation-projection (DoGIP), which is a novel matrix-free discretisation method of variational formulations introduce…
Energy-based comparison between the Fourier--Galerkin method and the finite element method
Jaroslav Vondřejc, Tom W. J. de Geus
The Fourier-Galerkin method (in short FFTH) has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom. Because the me…
Generalised Summation-by-Parts Operators and Variable Coefficients
Hendrik Ranocha
High-order methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is provided by summatio…
Stability of Correction Procedure via Reconstruction With Summation-by-Parts Operators for Burgers' Equation Using a Polynomial Chaos Approach
Philipp Öffner, Jan Glaubitz, Hendrik Ranocha
In this paper, we consider Burgers' equation with uncertain boundary and initial conditions. The polynomial chaos (PC) approach yields a hyperbolic system of deterministic equation…
Comparison of some Entropy Conservative Numerical Fluxes for the Euler Equations
Hendrik Ranocha
Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds o…