Related papers: A note on adjoint error estimation for one-dimensi…
Most identification laws of unknown parameters of linear regression equations (LRE) ensure only boundedness of a parametric error in the presence of additive perturbations, which is almost always unacceptable for practical scenarios. In…
Dynamic optimization is currently limited by sensitivity computations that require information from full forward and adjoint wave fields. Since the forward and adjoint solutions are computed in opposing time directions, the forward solution…
The paper contributes to strengthening the relation between machine learning and the theory of differential equations. In this context, the inverse problem of fitting the parameters, and the initial condition of a differential equation to…
The present contribution proves the asymptotic orbital stability of viscous regularizations of stable Riemann shocks of scalar balance laws, uniformly with respect to the viscosity/diffusion parameter $\epsilon$. The uniformity is…
We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…
Extending recent results in the isentropic case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the spectral stability of shock-wave solutions of the compressible Navier--Stokes…
This paper develops systematically the output feedback exponential stabilization for a one-dimensional unstable/anti-stable wave equation where the control boundary suffers from both internal nonlinear uncertainty and external disturbance.…
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…
We report on recent work on adaptive timestep control for weakly instationary gas flows [16, 18, 17] carried out within SFB 401, TPA3. The method which we implement and extend is a space-time splitting of adjoint error representations for…
We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…
We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the…
We complete the first step towards the resolution of several decades-old challenges in disturbance-robust adaptive control. For a scalar linear system with an unknown parameter for which no a priori bound is given, with a disturbance that…
In this work, we implement goal-oriented error control and spatial mesh adaptivity for stationary fluid-structure interaction. The a posteriori error estimator is realized using the dual-weighted residual method in which the adjoint…
Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and…
This work studies discontinuous Galerkin (DG) approximations of the boundary value problem for homogeneous transversely isotropic linear elastic bodies. Low-order approximations on triangles are adopted, with the use of three interior…
We consider asymptotically stable scalar difference equations with unit-norm initial conditions. First, it is shown that the solution may happen to deviate far away from the equilibrium point at finite time instants prior to converging to…
We develop novel stabilized cut discontinuous Galerkin (CutDG) methods for advection-reaction problems. The domain of interest is embedded into a structured, unfitted background mesh in $\mathbb{R}^d$ where the domain boundary can cut…
High fidelity simulations, e.g., large eddy simulation are often needed for accurately predicting pressure losses due to wake mixing in turbomachinery applications. An unsteady adjoint of such high fidelity simulations is useful for design…