An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in two space variables

DOI10.1016/0045-7825(86)90086-1zbMath0602.76097OpenAlexW2082693172MaRDI QIDQ1082210

Leszek F. Demkowicz, J. Tinsley Oden

Publication date: 1986

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(86)90086-1

zbMATH Keywords

Petrov-Galerkin methodmesh refinementadaptive schemespatial approximationconvection- dominated parabolic problemsconvection-dominated linear diffusionmethod of characteristics for the temporal approximationthree-dimensional space domainstime-dependent parabolic problemstruly local a posteriori error estimatestwo nonlinear Burgers' equations

Mathematics Subject Classification ID

Diffusion (76R50) Error bounds for boundary value problems involving PDEs (65N15) Heat equation (35K05) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Basic methods in fluid mechanics (76M99) Numerical methods for partial differential equations, boundary value problems (65N99)

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Cites Work

• Unnamed Item
• Unnamed Item
• Time-accurate solution of advection-diffusion problems by finite elements
• Approximate symmetrization and Petrov-Galerkin methods for diffusion- convection problems
• An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable
• On the transport-diffusion algorithm and its applications to the Navier-Stokes equations
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures

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