Least-squares spectral element method for non-linear hyperbolic differential equations

Authors:
B. De Maerschalck;M. I. Gerritsma
Affiliations:
Von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, 1640 Sint-Genesius-Rode, Belgium;Department of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 9
Cited 2

Least-squares finite element method for fluid dynamics

Computer Methods in Applied Mechanics and Engineering
Finite Element Methods of Least-Squares Type

SIAM Review
Least-squares spectral elements applied to the Stokes problem

Journal of Computational Physics
A Least-Squares Spectral Element Formulation for the Stokes Problem

Journal of Scientific Computing
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations

Journal of Computational Physics
Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

Journal of Computational Physics
Least-Squares Finite Element Methods and Algebraic Multigrid Solvers for Linear Hyperbolic PDEs

SIAM Journal on Scientific Computing
Numerical Conservation Properties of H(div)-Conforming Least-Squares Finite Element Methods for the Burgers Equation

SIAM Journal on Scientific Computing
Higher-Order Gauss---Lobatto Integration for Non-Linear Hyperbolic Equations

Journal of Scientific Computing

Simulation of thermal disturbances with finite wave speeds using a high order method

Journal of Computational and Applied Mathematics
Simulation of a natural circulation loop using a least squares hp-adaptive solver

Mathematics and Computers in Simulation

Quantified Score

Hi-index	7.29

Visualization

Abstract

The least-squares spectral element method has been applied to the one-dimensional inviscid Burgers equation which allows for discontinuous solutions. In order to achieve high order accuracy both in space and in time a space-time formulation has been applied. The Burgers equation has been discretized in three different ways: a non-conservative formulation, a conservative system with two variables and two equations: one first order linear PDE and one linearized algebraic equation, and finally a variant on this conservative formulation applied to a direct minimization with a QR-decomposition at elemental level. For all three formulations an h/p-convergence study has been performed and the results are discussed in this paper.