×

Implementation of an adaptive refinement technique for the SUPG algorithm. (English) Zbl 0596.73066

An adaptive refinement algorithm is developed and implemented for the SUPG method applied to a linear time-dependent advection problem in two space dimensions. Accuracy comparisons and timing results are presented which compare the adaptive solution and the solution obtained using a uniform mesh. The comparisons are made for the well-known rotating cone benchmark problem.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Oden, J.T.; Strouboulis, T.; Devloo, P., A moving-grid finite element algorithm for supersonic flow interaction between moving bodies, Comput. meths. appl. mech. engrg., 59, 235-255, (1986) · Zbl 0604.76052
[2] Carey, G.F.; Oden, J.T., Finite elements, computational aspects, (1983), Prentice-Hall Englewood Cliffs, NJ
[3] Hughes, T.J.R.; Brooks, A., A theoretical framework for Petrov Galerkin methods with discontinuous weighting functions. application to the streamline upwind procedure, (), 47-65
[4] Devloo, P.; Hayes, L.J., A fast vector algorithm for a matrix vector multiplication with the finite element method, ()
[5] Brooks, A.N.; Hughes, T.J.R., Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. meths. appl. mech. engrg., 32, 199-259, (1982) · Zbl 0497.76041
[6] Demkowicz, L.; Devloo, P.; Oden, J.T., On an h-type mesh refinement strategy based on minimisation of interpolation errors, Comput. meths. appl. mech. engrg., 53, 67-90, (1985) · Zbl 0556.73081
[7] R. Lohner, An adaptive finite element scheme for transient problems in CFD, Comput. Meths. Appl. Mech. Engrg. (to appear). · Zbl 0611.73079
[8] Morton, K.W., Generalised Galerkin methods for hyperbolic problems, Comput. meth. appl. mech. engrg., 52, 847-871, (1985) · Zbl 0568.76007
[9] Barrett, J.W.; Morton, K.W., Approximate symmetrization and Petrov-Galerkin methods for diffusionconvection problems, Comput. meths. appl. mech. engrg., 45, 97-122, (1984) · Zbl 0562.76086
[10] Bank, Randolph E.; Sherman, Andrew H., A refinement algorithm and dynamic data structure for finite element meshes, () · Zbl 0434.35008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.