Related papers: Higher-order time discretizations with ALE finite …
This paper presents a quasi-monolithic localized high-order arbitrary Lagrangian-Eulerian (qMLH-ALE) finite element method for multi-scale fluid-structure interaction (FSI) in microfluidic systems. The fluid momentum, the incompressible…
We apply exponential Runge Kutta time discretizations to semilinear evolution equations $\frac { {\rm d} U}{{\rm d} t}=AU+B(U)$ posed on a Hilbert space ${\mathcal Y}$. Here $A$ is normal and generates a strongly continuous semigroup, and…
We propose a numerical scheme to solve the time dependent linear Schr\"odinger equation. The discretization is carried out by combining a Runge-Kutta time-stepping scheme with a finite element discretization in space. Since the…
The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method builds upon the formulation introduced in Bertalmio et al., J. Comput. Phys., 174 (2001),…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
The numerical solution of the Stokes equations on an evolving domain with a moving boundary is studied based on the arbitrary Lagrangian-Eulerian finite element method and a second-order projection method along the trajectories of the…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
A new approach for the construction of high order A-stable explicit integrators for ordinary differential equations (ODEs) is theoretically studied. Basically, the integrators are obtained by splitting, at each time step, the solution of…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
We introduce a high-order finite element method for approximating the Vlasov-Poisson equations. This approach employs continuous Lagrange polynomials in space and explicit Runge-Kutta schemes for time discretization. To stabilize the…
In this paper, we propose a novel second-order dynamical low-rank mass-lumped finite element method for solving the Allen-Cahn (AC) equation, a semilinear parabolic partial differential equation. The matrix differential equation of the…
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,…
We study a discrete-time random feature method for nonlinear, time-dependent partial differential equations. In contrast to continuous-time formulations that treat time as an additional input variable, the method advances the solution step…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
With recent advances in variable-length structures for use in soft actuation, energy harvesting, energy dissipation and metamaterials, the mathematical modelling and numerical simulation of physical systems with time-varying domains is…
In Klingenberg, Schn\"ucke and Xia (Math. Comp. 86 (2017), 1203-1232) an arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) method to solve conservation laws has been developed and analyzed. In this paper, the ALE-DG method will…
We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This development extends an existing framework for well-posed problems and…
We present a novel (high-order) hybridizable discontinuous Galerkin (HDG) scheme for the fluid-structure interaction (FSI) problem. The (moving domain) incompressible Navier-Stokes equations are discretized using a divergence-free HDG…
In this paper we present a novel approach for the prescription of high order boundary conditions when approximating the solution of the Euler equations for compressible gas dynamics on curved moving domains. When dealing with curved…
In this paper, contrast-independent partially explicit time discretization for wave equations in heterogeneous high-contrast media via mass lumping is concerned. By employing a mass lumping scheme to diagonalize the mass matrix, the matrix…