Finite element methods for linear hyperbolic problems

• Published in: Computer methods in applied mechanics and engineering Vol. 45; no. 1; pp. 285 - 312
• Main Authors: Johnson, Claes, Nävert, Uno, Pitkäranta, Juhani
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.1984; Elsevier
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Physics; Turbulent flows, convection, and heat transfer; Finite element method; Diffusion; Convection; Hyperbolic equation
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/0045-7825(84)90158-0

Recent work by the authors on finite element methods for convection-diffusion problems and first-order linear hyperbolic problems is surveyed. A streamline diffusion method introduced by Hughes and Brooks which is higher-order accurate and has good stability properties is considered, giving proofs of global error estimates and localization results. Analogous results are given for the discontinuous Galerkin method. An extension of the streamline diffusion method to the time-dependent problem is given based on space-time elements with trial functions continuous in space and discontinuous in time. Finally, extensions of the streamline diffusion method to Friedrichs' systems is considered.