Motivated by the Discontinous Petrov-Galerkin method from [Numer. Methods Partial Differential Equations, 27 (2011), 70–105] by Demkowicz and Gopalakrishnan, we study a variational formulation of second order elliptic equations in mixed form, that is obtained by piecewise integrating one of the two equations in the system w.r.t. a partition of the domain into mesh cells. We apply a Petrov-Galer...

We consider the problem of optimal contracts in continuous time, when the agent’s actions are unobservable by the principal. We apply the stochastic maximum principle to give necessary conditions for optimal contracts, both for the case of the utility from the payoff being separable and not separable from the cost of the agent’s effort. The necessary conditions are shown also to be sufficient f...

This paper develops a high-order adaptive scheme for solving nonlinear Schrödinger equations. The solutions to such equations often exhibit solitary wave and local structures, which make adaptivity essential in improving the simulation efficiency. Our uses ultra-weak discontinuous Galerkin (DG) formulation belongs framework of multiresolution schemes. Various numerical experiments are presented...