TY - JOUR
T1 - Multi-Algorithmic Methods for Coupled Hyperbolic-Parabolic Problems
AU - Ern , A.
AU - Proft , J.
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 94
EP - 114
PY - 2006
DA - 2006/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/891.html
KW - discontinuous Galerkin, NIPG, interface conditions, porous media, coupled hyperbolic/parabolic PDE's.
AB - <p style="text-align: justify;">We study computational methods for linear, degenerate
advection-diffusion equations leading to coupled hyperbolic-parabolic
problems. A multi-algorithmic approach is proposed in which a different
approximation method is used locally depending on the mathematical
nature of the problem. Our analysis focuses on stability and a priori
error estimates of coupled continuous and discontinuous Galerkin
methods, achieving a global $h^{p+\frac{1}{2}}$ estimate. Both the mathematical
analysis and the numerical results demonstrate that careful
consideration is necessary when defining appropriate interface
conditions between the hyperbolic and parabolic regions.</p>