Related papers: Goal-oriented a posteriori estimation of numerical…
This work presents a numerical study of functional type a posteriori error estimates for IgA approximation schemes in the context of elliptic boundary-value problems. Along with the detailed discussion of the most crucial properties of such…
This paper proposes a metric for sets of trajectories to evaluate multi-object tracking algorithms that includes time-weighted costs for localisation errors of properly detected targets, for false targets, missed targets and track switches.…
We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for…
Two residual-type error estimators for the mortar staggered discontinuous Galerkin discretizations of second order elliptic equations are developed. Both error estimators are proved to be reliable and efficient. Key to the derivation of the…
A posteriori error estimators are studied for discontinuous Galerkin methods for solving a frictional contact problem, which is a representative elliptic variational inequality of the second kind. The estimators are derived by relating the…
We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…
We derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation accommodates both time evolving meshes and leapfrog based…
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it…
A semi-implicit-explicit (semi-IMEX) Runge-Kutta (RK) method is proposed for the numerical integration of ordinary differential equations (ODEs) of the form $\mathbf{u}' = \mathbf{f}(t,\mathbf{u}) + G(t,\mathbf{u}) \mathbf{u}$, where…
Solving the reactive low-Mach Navier-Stokes equations with high-order adaptive methods in time is still a challenging problem, in particular due to the handling of the algebraic variables involved in the mass constraint. We focus on the…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
We investigate the RG-time integration of the effective potential in the functional renormalization group in the presence of spontaneous symmetry breaking and its subsequent convexity restoration on the example of a scalar theory in $d=3$.…
Implicit Runge--Kutta (IRK) methods are highly effective for solving stiff ordinary differential equations (ODEs) but can be computationally expensive for large-scale problems due to the need of solving coupled algebraic equations at each…
This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems,…
This study computes the gradient of a function of numerical solutions of ordinary differential equations (ODEs) with respect to the initial condition. The adjoint method computes the gradient approximately by solving the corresponding…
We present a priori error estimates for a multirate time-stepping scheme for coupled differential equations. The discretization is based on Galerkin methods in time using two different time meshes for two parts of the problem. We aim at…
In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…
The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chain) and a computational challenge (multiple scales, large dynamical systems, time step…
We consider the a posteriori error analysis of approximations of parabolic problems based on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high-order discontinuous Galerkin temporal discretizations.…
Gradient temporal-difference (GTD) learning algorithms are widely used for off-policy policy evaluation with function approximation. However, existing convergence analyses rely on the restrictive assumption that the so-called feature…