Abstract. Starting from a recently developed energetic space-time weak formulation of boundary integral equations related to wave propagation problems defined on single and multidomains, a coupling algorithm is presented, which allows a flexible use of finite and boundary element methods as local discretization techniques, in order to efficiently treat unbounded multilayered media. Partial diff...

Using a relaxation strategy in a Lagrangian-Eulerian formulation, we propose a scheme in local conservation form for approximating weak solutions of complex compressible flows involving wave speeds of different orders of magnitude. Explicit time integration is performed on slow transport waves for the sake of accuracy while fast acoustic waves are dealt with implicitly to enable large time step...

We simplify the geometric interpretation of weak Ma-Trudinger-Wang condition for regularity in optimal transportation and provide a proof global c-convexity locally $c$-convex potentials when cost function $c$ is only assumed twice differentiable.

In this paper, we study the agent’s optimal quitting in a continuous-time principal-agent problem, where the agent is payed once at the end of the contract. In a jump diffusion setting, we formulate the agency problem as a combined optimal stopping and stochastic control problem in weak formulation. To find the solutions, we develop the classical verification theorem in terms of Variational Ine...

(1) A one-dimensional minimization problem and the Ritz method. (2) Weak formulation and the Galerkin method. Abstract error estimates. (3) The lemma of variations. Euler-Lagrange equations. Weak formulation, again. (4) The Ritz-Galerkin finite element method: philosophy. (5) The piecewise linear finite element space and basis functions. The linear system. (6) The piecewise linear finite elemen...

A general notion of evolutionary stability is formulated in models in which the possible behaviours are parameterized by a continuous variable, and selection is assumed to be weak. Two local stability conditions are formulated, m-stability and &stability, the former being first-order and the latter second-order in the mutant behavioural deviation. The conditions are interpreted in two standard ...

In this article, a numerical method is presented for computer assisted proofs to the existence and uniqueness of solutions to Dirichlet boundary value problems in a certain class of nonlinear elliptic equations. In a weak formulation of the problem, a weak solution is described as a zero point of a certain nonlinear map. Based on Newton-Kantorovich theorem, a numerical existence and local uniqu...