Related papers: Staggered explicit-implicit time-discretization fo…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
We propose a novel time stepping method for linear poroelasticity by extending a recent iterative decoupling approach to the second-order case. This results in a two-step scheme with an inner iteration and a relaxation step. We prove…
This paper proposes an adaptive time-stepping mothods for stochastic diffusion systems whose drift and diffusion coefficients are locally Lipschitz continuous and may exhibit polynomial growth. By controlling the growth of both the drift…
This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite…
The classical method for deriving the macroscopic dynamics of a lattice Boltzmann system is to use a combination of different approximations and expansions. Usually a Chapman-Enskog analysis is performed, either on the continuous Boltzmann…
We study in detail the pressure stabilizing effects of the non-iterated fixed-stress splitting in poromechanical problems which are nearly undrained and incompressible. When applied in conjunction with a spatial discretization which does…
Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGrote09}, a leapfrog based explicit local time-stepping…
Developing a macroscopic theory of elasto-plasticity in amorphous solids calls for (i) identifying the relevant macro state-variables and (ii) discriminating the different time-scales which characterize these variables. In current theories…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
We introduce a semi-explicit time-stepping scheme of second order for linear poroelasticity satisfying a weak coupling condition. Here, semi-explicit means that the system, which needs to be solved in each step, decouples and hence improves…
A coupled BEM/FEM formulation for the transient interaction between an acoustic field and a piezoelectric scatterer is proposed. The scattered part of the acoustic wave is represented in terms of retarded layer potentials while the elastic…
A variational time discretization of anisotropic Willmore flow combined with a spatial discretization via piecewise affine finite elements is presented. Here, both the energy and the metric underlying the gradient flow are anisotropic,…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
In this report it is shown that the implicit Euler time-discretization of some classes of switching systems with sliding modes, yields a very good stabilization of the trajectory and of its derivative on the sliding surface. Therefore the…
We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we…
Many interesting physical problems described by systems of hyperbolic conservation laws are stiff, and thus impose a very small time-step because of the restrictive CFL stability condition. In this case, one can exploit the superior…
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under…
By numerical integration, we study the relaxation dynamics of degenerate harmonic oscillator modes dispersively coupled to particle positions. Depending on whether the effective inertial potential induced by the oscillators keep the…