Mathematical Models and Methods in Applied Sciences · 2011 · 22 citations · 13 references
EngineeringComputational EngineeringMechanical EngineeringComputational Fluid DynamicsFinite Element AnalysisFinite Element MethodsConvection DynamicsConvergence AnalysisFinite Element DiscretizationFinite Element FormulationNumerical ConvergenceConvection-diffusionConvection-diffusion ModelingDiffusion EquationDiscretizationPetrov-galerkin DiscretizationTransient ConvectionUpwind SchemesUpwinding Schemes
We consider space semi-discretization of the transient convection–diffusion equation using a Streamline Upwind Petrov–Galerkin (SUPG) finite element method. We show stability and convergence both for the standard SUPG formulation with elementwise evaluated Laplacian and for a weakly consistent formulation where the elementwise Laplacian is replaced by a discrete, reconstructed, Laplacian. Some numerical examples are presented to illustrate the theory.
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A. Brooks, Thomas J.R. Hughes · Computer Methods in Applied Mechanics and Engineering · 1982 · 5.3K citations