The Dual Characteristic-Galerkin Method
Copyright policy )The Dual Characteristic-Galerkin Method
The Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and L 2 -stability in the case of Neumann boundary conditions. In a 2D numerical finite element setting (FEM), the method is compared to Primal Characteristic-Galerkin (PCGM), Streamline upwinding (SUPG), the Dual Discontinuous Galerkin method (DDG) and centered FEM without upwinding. DCGM is difficult to implement numerically but, in the numerical context of this note, it is far superior to all others.
- Laboratoire Jacques-Louis Lions France
- Sorbonne University France
- Sorbonne Paris Cité France
- SORBONNE UNIVERSITE France
- Sorbonne université France
Numerical methods (including Monte Carlo methods), 35Q35, 65M06, 65M15, 65M25, 65M60, Navier-Stokes equations for incompressible viscous fluids, finite element method, numerical method, convection-diffusion, Numerical Analysis (math.NA), PDEs in connection with fluid mechanics, Partial differential equations, Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, Diffusion, Error bounds for initial value and initial-boundary value problems involving PDEs, Mathematics - Analysis of PDEs, Derivative securities (option pricing, hedging, etc.), PDEs in connection with game theory, economics, social and behavioral sciences, Finite difference methods for initial value and initial-boundary value problems involving PDEs, QA1-939, partial differential equations, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Mathematics, Convection in hydrodynamic stability, Analysis of PDEs (math.AP)
Numerical methods (including Monte Carlo methods), 35Q35, 65M06, 65M15, 65M25, 65M60, Navier-Stokes equations for incompressible viscous fluids, finite element method, numerical method, convection-diffusion, Numerical Analysis (math.NA), PDEs in connection with fluid mechanics, Partial differential equations, Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, Diffusion, Error bounds for initial value and initial-boundary value problems involving PDEs, Mathematics - Analysis of PDEs, Derivative securities (option pricing, hedging, etc.), PDEs in connection with game theory, economics, social and behavioral sciences, Finite difference methods for initial value and initial-boundary value problems involving PDEs, QA1-939, partial differential equations, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Mathematics, Convection in hydrodynamic stability, Analysis of PDEs (math.AP)
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