Related papers: Local time steps for a finite volume scheme
We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation. Using local Fourier…
The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions…
A space-time fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes,…
One approach with rising popularity in analyzing time-dependent problems in science and engineering is the so-called space-time finite-element method that utilized finiteelements in both space and time. A common ansatz in this context is to…
In this work, we propose a mixed finite element method for solving elliptic multiscale problems based on a localized orthogonal decomposition (LOD) of Raviart-Thomas finite element spaces. It requires to solve local problems in small…
In this paper, we propose a discretization for the (nonlinearized) compressible Stokes problem with a linear equation of state $\rho=p$, based on Crouzeix-Raviart elements. The approximation of the momentum balance is obtained by usual…
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…
In this paper, we develop a scaled gradient-momentum framework for continuous-time optimization that achieves global finite-time convergence. A state-dependent scaling mechanism is introduced to enable classical dynamics, such as…
We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to…
We propose a novel collocated projection method for solving the incompressible Navier-Stokes equations with arbitrary boundaries. Our approach employs non-graded octree grids, where all variables are stored at the nodes. To discretize the…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to…
Most numerical schemes proposed for solving BGK models for rarefied gas dynamics are based on the discrete velocity approximation. Since such approach uses fixed velocity grids, one must secure a sufficiently large domain with fine velocity…
With the increasing number of components and further miniaturization the mean time between faults in supercomputers will decrease. System level fault tolerance techniques are expensive and cost energy, since they are often based on…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and…
We present an adaptive finite element method for the incompressible Navier--Stokes equations based on a standard splitting scheme (the incremental pressure correction scheme). The presented method combines the efficiency and simplicity of a…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
In this work we prove that weak solutions constructed by a variational multiscale method are suitable in the sense of Scheffer. In order to prove this result, we consider a subgrid model that enforces orthogonality between subgrid and…