Finite difference approximations of multidimensional unsteady convection-diffusion-reaction equations

DOI10.1016/J.JCP.2015.01.024zbMath1354.65168OpenAlexW1982500459MaRDI QIDQ729094

Adem Kaya

Publication date: 20 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2015.01.024

zbMATH Keywords

finite element methodfinite difference methodunsteady convection-diffusion-reaction

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (16)

High order numerical algorithms based on biquadratic spline collocation for two-dimensional parabolic partial differential equations ⋮ Finite difference approximations of multidimensional convection-diffusion-reaction problems with small diffusion on a special grid ⋮ Numerical Solution of Two-Dimensional Advection–Diffusion Equation Using Generalized Integral Representation Method ⋮ Systematic formulation of a general numerical framework for solving the two-dimensional convection-diffusion-reaction system ⋮ New DY-HS hybrid conjugate gradient algorithm for solving optimization problem of unsteady partial differential equations with convection term ⋮ Sixth-Order Adaptive Non-uniform Grids for Singularly Perturbed Boundary Value Problems ⋮ Higher order nonuniform grids for singularly perturbed convection-diffusion-reaction problems ⋮ Fast IIF-WENO method on non-uniform meshes for nonlinear space-fractional convection-diffusion-reaction equations ⋮ Local knot method for 2D and 3D convection-diffusion-reaction equations in arbitrary domains ⋮ A novel meshless method for fully nonlinear advection-diffusion-reaction problems to model transfer in anisotropic media ⋮ Conditional full stability of positivity-preserving finite difference scheme for diffusion-advection-reaction models ⋮ Fourth kind shifted Chebyshev polynomials for solving space fractional order advection-dispersion equation based on collocation method and finite difference approximation ⋮ Half boundary method for steady state convection-diffusion equations with different boundary conditions ⋮ Stability and error estimates of a new high-order compact ADI method for the unsteady 3D convection-diffusion equation ⋮ An adaptive variational multiscale element free Galerkin method based on the residual-based a posteriori error estimators for convection-diffusion-reaction problems ⋮ Anisotropic mesh adaptation for steady convection-dominated problems based on bubble-type local mesh generation

Cites Work

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• An adaptive finite element method for evolutionary convection dominated problems
• An adaptive SUPG method for evolutionary convection-diffusion equations
• Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion
• Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reaction problems
• Applications of the pseudo residual-free bubbles to the stabilization of convection-diffusion-reaction problems
• Coupling stabilized finite element methods with finite difference time integration for advection-diffusion-reaction problems
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• On the stability of residual-free bubbles for convection-diffusion problems and their approximation by a two-level finite element method
• Applications of the pseudo residual-free bubbles to the stabilization of convection-diffusion problems
• Weighted essentially non-oscillatory schemes
• A finite difference scheme for multidimensional convection-diffusion-reaction equations
• On the choice of a stabilizing subgrid for convection-diffusion problems
• Stabilized finite element methods for singularly perturbed parabolic problems
• Comparison of some finite element methods for solving the diffusion-convection-reaction equation
• Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.)
• Finite difference approximations of multidimensional convection-diffusion-reaction problems with small diffusion on a special grid
• LINK-CUTTING BUBBLES FOR THE STABILIZATION OF CONVECTION-DIFFUSION-REACTION PROBLEMS

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