Related papers: Adaptive timestep control for nonstationary soluti…
A residual error estimator is proposed for the energy norm of the error for a scalar reaction-diffusion problem and for the monodomain model used in cardiac electrophysiology. The problem is discretized using $P_1$ finite elements in space,…
We present a family of integral equation-based solvers for the heat equation, reaction-diffusion systems, the unsteady Stokes equation and the incompressible Navier-Stokes equations in two space dimensions. Our emphasis is on the…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…
In this work, we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo's form. The L1 implicit scheme is shown to preserve a variational energy dissipation law on arbitrary nonuniform…
The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…
We propose a PDE-controllability based approach to the enhancement of diffusive mixing for passive scalar fields. Unlike in the existing literature, our relaxation enhancing fields are not prescribed $\textit{ab initio}$ at every time and…
In this paper, we present a new control model for optimizing pressure and water quality operations in water distribution networks. Our formulation imposes a set of time-coupling constraints to manage temporal pressure variations, which are…
We shall develop a fully discrete space-time adaptive method for linear parabolic problems based on new reliable and efficient a posteriori analysis for higher order dG(s) finite element discretisations. The adaptive strategy is motivated…
The Reynolds-Averaged Navier-Stokes equations and the Large-Eddy Simulation equations can be coupled using a transition function to switch from a set of equations applied in some areas of a domain to the other set in the other part of the…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…
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…
This article is concerned with the discretisation of the Stokes equations on time-dependent domains in an Eulerian coordinate framework. Our work can be seen as an extension of a recent paper by Lehrenfeld & Olshanskii [ESAIM: M2AN,…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
The Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions (PNP-FBV) describe ion transport with Faradaic reactions and have applications in a wide variety of fields. Using an adaptive time-stepper based…
An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal model. The suggested method is proved to preserve a modified energy dissipation law at the discrete levels if the time-step ratios…
In this work, we present an efficient approach for the spatial and temporal discretization of the nonlocal Allen-Cahn equation, which incorporates various double-well potentials and an integrable kernel, with a particular focus on a…