We derive local error estimates for the discretization of optimal control problems governed by linear advection-diffusion partial differential equations (PDEs) using the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method. We show that if the SUPG method is used to solve optimization problems governed by an advection-dominated PDE the convergence properties of the SUPG met...

Deterministic chaotic dynamics presumes that the state space can be partitioned arbitrarily finely. In a physical system, the inevitable presence of some noise sets a finite limit to the finest possible resolution that can be attained. Much previous research deals with what this attainable resolution might be, all of it based on a global averages over stochastic flow. We show how to compute the...

In this paper, an adjoint-based error estimation and mesh adaptation framework is developed for the compressible inviscid flows. The algorithm employs the Finite Calculus (FIC) scheme for the numerical solution of the flow and discrete adjoint equations in the context of the Galerkin finite element method (FEM) on triangular grids. The FIC scheme treats the instabilities normally generated in t...

Adjoint methods are widely used in various areas of computational science to efficiently obtain sensitivities of functionals which result from the solution of partial differential equations (PDEs). In addition, adjoint methods have been used in other settings including error estimation, uncertainty quantification and inverse problem formulations. When deriving the adjoint equations, there are t...

An adjoint-based output error estimation algorithm is presented for unsteady problems discretized on static meshes with a space-time discontinuous Galerkin finite element method. An approximate factorization technique is used to solve both the forward and the discrete adjoint problems. A space-time anisotropy measure based on projection of the adjoint solution is used to attribute the error to ...

A discrete-adjoint formulation is presented for the three-dimensional Euler equations discretized on a Cartesian mesh with embedded boundaries. The solution algorithm for the adjoint and flow-sensitivity equations leverages the Runge–Kutta time-marching scheme in conjunction with the parallel multigrid method of the flow solver. The matrix-vector products associated with the linearization of th...

The optimal checkpointing algorithm (Griewank and Walther, 2000) minimizes the computational complexity of the adjoint state method. Applied to reverse time migration, optimal checkpointing eliminates (or at least drastically reduces) the need for disk i/o, which is quite extensive in more straightforward implementations. This paper describes optimal checkpointing in a form which applies both t...

Hydrocarbon production modifies the stress conditions in the subsurface and changes the model parameters previously estimated from the prospect. The capability to remotely monitor the changes in the reservoir using seismic data has strategic importance since it allows us to infer fluid movement and evolution of stress conditions, which are key factors to enhance recovery and reduce uncertainty ...

The adjoint method provides a computationally efficient means of calculating the gradient for applications in constrained optimization. In this article, we consider a network of scalar conservation laws with general topology, whose behavior is modified by a set of control parameters in order to minimize a given objective function. After discretizing the corresponding partial differential equati...