Search results for "nonlinear boundary conditions"
showing 3 items of 3 documents
Existence and Regularity for a Class of Nonlinear Hyperbolic Boundary Value Problems
2002
AbstractThe regularity of the solution of the telegraph system with nonlinear monotone boundary conditions is investigated by two methods. The first one is based on D'Alembert-type representation formulae for the solution. In the second method the telegraph system is reduced to a linear Cauchy problem with a locally Lipschitzian functional perturbation; then regularity results are established by appealing to the theory of linear semigroups.
A posteriori error estimates for variational problems in the theory of viscous fluids
2016
The papers included in the thesis are focused on functional type a posteriori error estimates for the Stokes problem, the Stokes problem with friction type boundary conditions, the Oseen problem, and the anti-plane Bingham problem. In the summary of the thesis we consider only the Oseen problem. The papers present and justify special forms of these estimates which are suitable for the approximations generated by the Uzawa algorithm. The estimates are of two main types. Estimates of the first type use exact solutions obtained on the steps of the Uzawa algorithm. They show how errors encompassed in Uzawa approximations behave and have mainly theoretical meaning. Estimates of the second type o…
Convergence of the finite volume method for a conductive-radiative heat transfer problem
2013
We show that the finite volume method rigorously converges to the solution of a conductive-radiative heat transfer problem with nonlocal and nonlinear boundary conditions. To get this result, we start by proving existence of solutions for a finite volume discretization of the original problem. Then, by obtaining uniform boundedness of discrete solutions and their discrete gradients with respect to mesh size, we finally get L 2type convergence of discrete solutions.