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In the present paper we deal with parabolic fractional initial-boundary value problems of Sturm Liouville type in an interval and in a general star graph. We first give several existence, uniqueness and regularity results of weak and…

Analysis of PDEs · Mathematics 2022-03-02 G. Leugering , G. Mophou , M. Moutamal , M. Warma

Parabolic optimal control problems arise in numerous scientific and engineering applications. They typically lead to large-scale coupled forward-backward systems that cannot be treated with classical time-stepping schemes and are…

Numerical Analysis · Mathematics 2026-03-10 Liu-Di Lu , Tommaso Vanzan

Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…

Numerical Analysis · Mathematics 2013-06-05 Maziar Raissi , Padmanabhan Seshaiyer

The trajectory optimization of the atmospheric entry of a reusable launch vehicle is studied. The objective is to maximize the crossrange of the vehicle subject to two control-inequality path constraints, two state-inequality path…

Optimization and Control · Mathematics 2024-06-07 Cale A. Byczkowski , Anil V. Rao

In this paper, we present a method that enables to solve in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

Optimization and Control · Mathematics 2011-10-19 Yvon Maday , Julien Salomon , Kamel Riahi

We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme)…

Numerical Analysis · Mathematics 2018-08-17 Dominik Meidner , Boris Vexler

Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients…

Numerical Analysis · Mathematics 2022-02-04 Balázs Kovács , Buyang Li

For unconstrained control problems, a local convergence rate is established for an $hp$-method based on collocation at the Radau quadrature points in each mesh interval of the discretization. If the continuous problem has a sufficiently…

Numerical Analysis · Mathematics 2021-07-20 William W. Hager , Hongyan Hou , Subhashree Mohapatra , Anil V. Rao

This paper investigates numerical methods for solving stochastic linear quadratic (SLQ) optimal control problems governed by stochastic partial differential equations (SPDEs). Two distinct approaches, the open-loop and closed-loop ones, are…

Optimization and Control · Mathematics 2024-11-19 Andreas Prohl , Yanqing Wang

In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…

Numerical Analysis · Mathematics 2018-10-09 Jerome Droniou , Neela Nataraj , Devika Shylaja

We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…

Numerical Analysis · Mathematics 2023-12-20 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…

Optimization and Control · Mathematics 2010-08-24 Morten Vierling

We consider the numerical approximation of a nonlinear system of partial differential equations modeling magnetostriction in the small-strain regime consisting of the Landau--Lifshitz--Gilbert equation for the magnetization and the…

Numerical Analysis · Mathematics 2026-04-01 Martin Kružík , Hywel Normington , Michele Ruggeri

In this paper we consider the numerical approximation of a general second order semi-linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media. Using finite element…

Numerical Analysis · Mathematics 2020-11-18 Jean Daniel Mukam , Antoine Tambue

We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…

Optimization and Control · Mathematics 2024-01-19 Christoph Buchheim , Alexandra Grütering , Christian Meyer

We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…

Numerical Analysis · Mathematics 2023-03-01 Pelin Çiloğlu , Hamdullah Yücel

We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…

Numerical Analysis · Mathematics 2020-03-23 Ulrich Langer , Andreas Schafelner

We study the effect of the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method on the discretization of optimal control problems governed by linear advection-diffusion equations. We compare two approaches for the…

Numerical Analysis · Mathematics 2024-11-18 S. Scott Collis , Matthias Heinkenschloss

We analyze the finite element discretization of distributed elliptic optimal control problems with variable energy regularization, where the usual $L^2(\Omega)$ norm regularization term with a constant regularization parameter $\varrho$ is…

Numerical Analysis · Mathematics 2023-08-15 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…

Numerical Analysis · Mathematics 2025-03-03 Herbert Egger , Andreas Schafelner