Characteristic mixed discontinuous finite element methods for advection-dominated diffusion problems

Computer Methods in Applied Mechanics and Engineering

Volumn 191, Issue 23-24, 2002, Pages 2509-2538

  Chen, Zhangxin ^a  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

Author keywords

Advection dominated diffusion problems; Characteristics based methods; CMFEM; Convergence; ELLAM; Equivalence; Mixed discontinuous finite element methods; MMOC; MMOCAA; Stability

Indexed keywords

DIFFUSION; ERROR ANALYSIS; FINITE ELEMENT METHOD; LAGRANGE MULTIPLIERS;

ADVECTION-DOMINATED DIFFUSION;

MECHANICAL ENGINEERING;

ADVECTION; DIFFUSION; FINITE ELEMENT METHOD;

EID: 0037192724     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(01)00411-X     Document Type: Article

References (42)

1. A characteristics-mixed finite element for advection-dominated transport problems
2. An interior penalty finite element method with discontinuous elements
3. Nonconforming elements in the finite element method with penalty
4. Finite element methods for elliptic equations using nonconforming elements
5. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
6. Parallel, adaptive finite element methods for conservation laws
7. Discontinuous Galerkin approximations for elliptic problems
8. An Eulerian Lagrangian localized adjoint method for the advection-diffusion equation
9. BDM mixed methods for a nonlinear elliptic problem
10. On the relationship of various discontinuous finite element methods for second-order elliptic equations
11. Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode
12. Mixed-RKDG finite element methods for the 2D hydrodynamic model for semiconductor device simulation
13. Error analysis for characteristics-based methods for degenerate parabolic problems
14. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: General framework
15. The local discontinuous Galerkin method for time-dependent convection-diffusion systems
16. Some improved error estimates for the modified method of characteristics
17. An implicit matching principle for global element calculations
18. Interior penalty procedures for elliptic and parabolic Galerkin methods
19. The approximation of the pressure by a mixed method in the simulation of miscible displacement
20. On the numerical simulation of water flooding of heterogeneous petroleum reservoirs
21. A locally conservative Eulerian-Lagrangian numerical method and its application to nonlinear transport in porous media
22. Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures
23. Adaptive finite element methods for parabolic problems 1: A linear model problems
24. Time discretization of parabolic problems by the discontinuous Galerkin method
25. Explicit finite element methods for symmetric hyperbolic equations
26. An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
27. On a finite element method for solving the neutron transport equation
28. 3
29. A discontinuous hp finite element method for diffusion problems
30. On the transport-diffusion algorithm and its application to the Navier-Stokes equations
31. A mixed finite element method for second order elliptic problems
32. Triangular mesh methods for the neutron transport equation
33. An optimal-order error estimate for the discontinuous Galerkin method
34. Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems
35. Some new families of finite elements for the Stokes equations
36. An ELLAM scheme for advection-diffusion equations in two dimensions
37. An elliptic collocation-finite element method with interior penalties