Search results for " Exact solutions"
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A Posteriori Error Bounds for Approximations of the Oseen Problem and Applications to the Uzawa Iteration Algorithm
2014
Abstract. We derive computable bounds of deviations from the exact solution of the stationary Oseen problem. They are applied to approximations generated by the Uzawa iteration method. Also, we derive an advanced form of the estimate, which takes into account approximation errors arising due to discretization of the boundary value problem, generated by the main step of the Uzawa method. Numerical tests confirm our theoretical results and show practical applicability of the estimates.
On a radiating fluid in a general relativistic context
2006
A model for the radiation hydrodynamics in general relativity is analyzed, describing the gravitational collapse and supernovae explosion. As these physical phenomena can be assumed spherically symmetric, the equations of motion for a unique fluid, representing the interaction between matter and radiation, are written in a spherical symmetric space-time with respect to a comoving frame. The system is completed by using the Eddington closure, assuming a local thermodynamical equilibrium for the radiation field. The resulting system is analyzed by the Lie symmetry approach and a reduction to an ODEs system is obtained. Numerical simulations of the solutions are performed, showing a realistic …