Finite-volume schemes for Friedrichs systems in multiple space dimensions:A priori anda posteriori error estimates

2004 ◽  
Vol 21 (1) ◽  
pp. 104-131 ◽  
Author(s):  
Vladimir Jovanovi? ◽  
Christian Rohde
Keyword(s):  
Error Estimates ◽  
Finite Volume ◽  
Posteriori Error ◽  
Finite Volume Schemes ◽  
Friedrichs Systems

Numerical Entropy and Adaptivity for Finite Volume Schemes

2011 ◽  
Vol 10 (5) ◽  
pp. 1132-1160 ◽  
Author(s):  
Gabriella Puppo ◽  
Matteo Semplice
Keyword(s):  
Finite Volume ◽  
Adaptive Strategy ◽  
Posteriori Error ◽  
Uniform Grid ◽  
Finite Volume Schemes ◽  
Adaptive Scheme ◽  
Systems Of Conservation Laws ◽  
Order Scheme ◽  
Production Of Entropy ◽  
Numerical Entropy

AbstractWe propose an a-posteriori error/smoothness indicator for standard semi-discrete finite volume schemes for systems of conservation laws, based on the numerical production of entropy. This idea extends previous work by the first author limited to central finite volume schemes on staggered grids. We prove that the indicator converges to zero with the same rate of the error of the underlying numerical scheme on smooth flows under grid refinement. We construct and test an adaptive scheme for systems of equations in which the mesh is driven by the entropy indicator. The adaptive scheme uses a single nonuniform grid with a variable timestep. We show how to implement a second order scheme on such a space-time non uniform grid, preserving accuracy and conservation properties. We also give an example of a p-adaptive strategy.

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