On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toeplitz matrices.
On traces of solutions of a semilinear partial differential equation of elliptic type
On two problems studied by A. Ambrosetti
We study the Ambrosetti–Prodi and Ambrosetti–Rabinowitz problems.We prove for the first one the existence of a continuum of solutions with shape of a reflected (-shape). Next, we show that there is a relationship between these two problems.
One iterative method concerning the solution of Dirichlet's problem
One-dimensional model for surface gravitational waves in a mountain reservoir.
One-sided resonance for quasilinear problems with asymmetric nonlinearities.
Opérateurs intégraux de Fourier et le problème de la dérivée oblique
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting...
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from...
Optimal control of fluid flow in soil 1. Deterministic case.
We study the numerical aspect of the optimal control of problems governed by a linear elliptic partial differential equation (PDE). We consider here the gas flow in porous media. The observed variable is the flow field we want to maximize in a given part of the domain or its boundary. The control variable is the pressure at one part of the boundary or the discharges of some wells located in the interior of the domain. The objective functional is a balance between the norm of the flux in the observation...
Optimal convergence rates of mortar finite element methods for second-order elliptic problems
Optimal convergence rates of hp mortar finite element methods for second-order elliptic problems
We present an improved, near-optimal hp error estimate for a non-conforming finite element method, called the mortar method (M0). We also present a new hp mortaring technique, called the mortar method (MP), and derive h, p and hp error estimates for it, in the presence of quasiuniform and non-quasiuniform meshes. Our theoretical results, augmented by the computational evidence we present, show that like (M0), (MP) is also a viable mortaring technique for the hp method.
Optimal error estimation for Petrov-Galerkin methods in two dimensions.
Optimal grids for anisotropic problems.
Optimal L...-Error Estimates for Nonconforming and Mixed Finite Element Methods of Lowest Order.
Optimal L...-Error Estimates for Piecewise Linear Finite Elements in Irn for 1...n...3.
Optimal Lyapunov inequalities and applications to nonlinear problems
Optimal stability for inverse elliptic boundary value problems with unknown boundaries
Optimization in problems involving the -Laplacian.
Optimization of the domain in elliptic problems by the dual finite element method
An optimal part of the boundary of a plane domain for the Poisson equation with mixed boundary conditions is to be found. The cost functional is (i) the internal energy, (ii) the norm of the external flux through the unknown boundary. For the numerical solution of the state problem a dual variational formulation - in terms of the gradient of the solution - and spaces of divergence-free piecewise linear finite elements are used. The existence of an optimal domain and some convergence results are...