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Volume 3, Issue 1
Multi-Algorithmic Methods for Coupled Hyperbolic-Parabolic Problems

A. Ern & J. Proft

Int. J. Numer. Anal. Mod., 3 (2006), pp. 94-114.

Published online: 2006-03

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  • Abstract

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.

  • Keywords

discontinuous Galerkin, NIPG, interface conditions, porous media, coupled hyperbolic/parabolic PDE's.

  • AMS Subject Headings

35R35, 35N

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-94, author = {Ern , A. and Proft , J.}, title = {Multi-Algorithmic Methods for Coupled Hyperbolic-Parabolic Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {1}, pages = {94--114}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/891.html} }
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 -

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.

A. Ern & J. Proft. (1970). Multi-Algorithmic Methods for Coupled Hyperbolic-Parabolic Problems. International Journal of Numerical Analysis and Modeling. 3 (1). 94-114. doi:
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