Local projection methods on layer-adapted meshes for higher order discretisations of convection–diffusion problems

2009 ◽  
Vol 59 (10) ◽  
pp. 2515-2533 ◽  
Author(s):  
Gunar Matthies
Keyword(s):  
Projection Methods ◽  
Higher Order ◽  
Local Projection ◽  
Convection Diffusion ◽  
Diffusion Problems

Error estimates for higher-order finite volume schemes for convection–diffusion problems

2018 ◽  
Vol 26 (1) ◽  
pp. 35-62
Author(s):  
Dietmar Kröner ◽  
Mirko Rokyta
Keyword(s):  
Error Estimates ◽  
Finite Volume ◽  
Original Problem ◽  
A Priori ◽  
Higher Order ◽  
Finite Volume Schemes ◽  
Convection Diffusion ◽  
Type Reconstruction ◽  
Convection Dominated ◽  
Diffusion Problems

AbstractIt is still an open problem to provea priorierror estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domainΩin ℝ2and we can prove such kind of ana priorierror estimate. In the part of the estimate, which refers to the discretization of the convective term, we gainh1/2. Although the original problem is linear, the numerical problem becomes nonlinear, due to MUSCL type reconstruction/limiter technique.

Improved Applications of Relaxation Schemes for Hyperbolic Systems of Conservation Laws and Convection-diffusion Problems

2006 ◽  
Vol 6 (1) ◽  
pp. 56-86 ◽  
Author(s):  
Mohammed Seaïd
Keyword(s):  
Conservation Laws ◽  
Stokes Equations ◽  
Hyperbolic Systems ◽  
Time Integration ◽  
Higher Order ◽  
Convection Diffusion ◽  
Order Reconstruction ◽  
Relaxation Schemes ◽  
Systems Of Conservation Laws ◽  
Diffusion Problems

AbstractA class of third-order relaxation schemes for hyperbolic systems of conservation laws with source terms is reconstructed. The schemes employ general higher-order reconstruction for spatial discretization and higher-order implicit-explicit schemes or TVD Runge — Kutta schemes for time integration of relaxed systems. Extension to multidimensional convection-diffusion problems is also included in this paper. Numerical results for inviscid gas Euler equations, shallow water and incompressible Navier — Stokes equations are given in both one and two space dimensions.

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