TY - JOUR
T1 - Numerical Issues in the Implementation of High Order Polynomial Multi-Domain Penalty Spectral Galerkin Methods for Hyperbolic Conservation Laws
AU - Sigal Gottlieb & Jae-Hun Jung
JO - Communications in Computational Physics
VL - 2-4
SP - 600
EP - 619
PY - 2009
DA - 2009/02
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7752.html
KW - 
AB - <p style="text-align: justify;">In this paper, we consider high order multi-domain penalty spectral Galerkin
methods for the approximation of hyperbolic conservation laws. This formulation has
a penalty parameter which can vary in space and time, allowing for flexibility in the
penalty formulation. This flexibility is particularly advantageous for problems with
an inhomogeneous mesh. We show that the discontinuous Galerkin method is equivalent to the multi-domain spectral penalty Galerkin method with a particular value of
the penalty parameter. The penalty parameter has an effect on both the accuracy and
stability of the method. We examine the numerical issues which arise in the implementation of high order multi-domain penalty spectral Galerkin methods. The coefficient
truncation method is proposed to prevent the rapid error growth due to round-off
errors when high order polynomials are used. Finally, we show that an inconsistent
evaluation of the integrals in the penalty method may lead to growth of errors. Numerical examples for linear and nonlinear problems are presented.</p>