Remarks on $L^2$-well-posed mixed problems for hyperbolic equations of second order

A class of well-posed approximations for constrained second order hyperbolic equations

The purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on the solution. The principle is a singular modification of the mass matrix obtained by the mean of different discretizations of the solution and of its time derivative. The major interest of these methods is ...

An H-galerkin Mixed Method for Second Order Hyperbolic Equations

An H1Galerkin mixed finite element method is discussed for a class of second order hyperbolic problems. It is proved that the Galerkin approximations have the same rates of convergence as in the classical mixed method, but without LBB stability condition and quasi-uniformity requirement on the finite element mesh. Compared to the results proved for one space variable, the L∞(L2)-estimate of the...

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

On Solvability of Ill Posed Initial–boundary Value Problems for Higher Order Nonlinear Hyperbolic Equations

Grid Modification for Second Order Hyperbolic Problems

A family of Galerkin nite element methods is presented to accurately and e ciently solve the wave equation that includes sharp propagating wave fronts. The new methodology involves di erent nite element discretizations at di erent time levels; thus, at any time level, relatively coarse grids can be applied in regions where the solution changes smoothly while ner grids can be employed near wave ...