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In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
The single-step one-shot method has proven to be very efficient for PDE-constrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization…
The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to…
This paper introduces a new framework for analyzing the stability of discrete-time model predictive controllers acting on continuous-time systems. The proposed framework introduces the distinction between discretization time (used to…
Model Predictive Control (MPC) is a versatile approach capable of accommodating diverse control requirements that holds significant promise for a broad spectrum of industrial applications. Noteworthy challenges associated with MPC include…
We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which a mesh relaxation time \tau is employed as a…
In this paper, we address the efficient implementation of moving horizon state estimation of constrained discrete-time linear systems. We propose a novel iteration scheme which employs a proximity-based formulation of the underlying…
We present a methodology for simulating dilute suspensions of particles settling under gravity, with the main purpose of overcoming limitations of triply periodic configurations, mainly the strong vertical correlation that hinders the study…
This paper presents original and close to optimal stability conditions linking the time step and the space step, stronger than the CFL criterion: $\delta t\leq C\delta x^\alpha$ with $\alpha=\frac{2r}{2r-1}$, $r$ an integer, for some…
In this paper, we present an efficient numerical method to address a thermodynamically consistent gas flow model in porous media involving compressible gas and deformable rock. The accurate modeling of gas flow in porous media often poses…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…
We consider suspensions of rigid bodies in a two-dimensional viscous fluid. Even with high-fidelity numerical methods, unphysical contact between particles occurs because of spatial and temporal discretization errors. We apply the method of…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…
The safety of rotorcraft operating in cold environments is jeopardised by the possibility of ice accretion on the rotor blades. Eventually, ice can shed from the blade due to the high centrifugal forces and impact other parts of the…
In this paper, we propose a new numerical strategy for the stabilization of evolution systems. The method is based on the methodology given by Ammari, Nicaise andPignotti in ''Stabilization by switching time-delay, Asymptot. Anal., 83…
In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
The susceptibility of timestepping algorithms to numerical instabilities is an important consideration when simulating partial differential equations (PDEs). Here we identify and analyze a pernicious numerical instability arising in…