Accelerated finite elements schemes for parabolic stochastic partial differential equations

It is our purpose here to contribute further to the analysis of some of the above questions by proving the existence, and in some cases the uniqueness, of global and local

A surgical spatula within the defect (introduced from the right atrial side) demonstrates the communication (dashed arrow) to the left ventricle just below the right coronary

0.4.2 Chapitre 2 : Simulations num´ eriques de l’´ equation de Burgers non visqueuse avec des conditions aux limites p´ eriodiques et un terme source stochastique 6 0.4.3 Chapitre 3

The study of the behavior of the parareal algorithm when the linear implicit Euler scheme is chosen as the coarse integrator is provided in Section 4: more precisely, see Theorem

In this section we review the concept of partitioned Runge-Kutta methods and derive a new class of semi-implicit R-K schemes, and we propose several schemes up to third order

For both the relative l 2 -error and the l ∞ -error we can again see that the essentially high-order compact schemes have significantly lower error values and higher convergence

Such a behavior is referred here to has a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions

Key words: Quasi-linear Parabolic PDEs, Hyperbolic PDEs systems, Vanishing viscosity method, Smooth solutions, Stochastic Calculus, Feynman-Kac Formula, Girsanov’s Theorem..