Related papers: Semi-implicit Euler schemes for ordinary different…
We study discretization of Darboux integrable systems. The discretization is done by using $x$- or $y$-integrals of the considered systems. New examples of semi-discrete Darboux integrable systems are obtained.
A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these…
This work presents a novel interpolation-free mesh adaptation technique for the Euler equations within the arbitrary Lagrangian Eulerian framework. For the spatial discretization, we consider a residual distribution scheme, which provides a…
Implicit schemes have been extensively used in building physics to compute the solution of moisture diffusion problems in porous materials for improving stability conditions. Nevertheless, these schemes require important sub-iterations when…
The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We…
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…
The present work concerns the derivation of a numerical scheme to approximate weak solutions of the Euler equations with a gravitational source term. The designed scheme is proved to be fully well-balanced since it is able to exactly…
We establish a discrete operator--theoretic framework for the analysis of implicit Euler and Lie--Trotter splitting schemes for delay differential equations (DDEs). Both schemes are formulated in terms of discrete resolvent operators acting…
Recent advances show that semi-supervised implicit representation learning can be achieved through physical constraints like Eikonal equations. However, this scheme has not yet been successfully used for LiDAR point cloud data, due to its…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
In this paper we consider fully discrete approximations with inf-sup stable mixed finite element methods in space to approximate the Navier-Stokes equations. A continuous downscaling data assimilation algorithm is analyzed in which…
A procedure is suggested for testing the resolution and comparing the relative accuracy of numerical schemes for integration of the incompressible Euler equations.
In this work, we introduce semi-implicit or implicit finite difference schemes for the continuity equation with a gradient flow structure. Examples of such equations include the linear Fokker-Planck equation and the Keller-Segel equations.…
The 2D Euler equations are a simple but rich set of non-linear PDEs that describe the evolution of an ideal inviscid fluid, for which one dimension is negligible. Solving numerically these equations can be extremely demanding. Several…
Discretization methods for differential-algebraic equations (DAEs) are considered that are based on the integration of an associated inherent ordinary differential equation (ODE). This allows to make use of any discretization scheme…
In this paper, we extend the implicit-explicit (IMEX) methods of Peer type recently developed in [Lang, Hundsdorfer, J. Comp. Phys., 337:203--215, 2017] to a broader class of two-step methods that allow the construction of super-convergent…
In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Ku\v{c}era (JCP 2007) as well as the class of RS-IMEX schemes. The implicit part is based on a Jacobian matrix which is…
We consider a non-linear extension of Biot's model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. We perform an implicit discretization in time (backward Euler) and propose two…
This paper is concerned with the numerical approximation of stochastic mechanical systems with nonlinear holonomic constraints. Such systems are described by second order stochastic differential-algebraic equations involving an implicitly…
We propose a semi-discrete scheme for 2D Keller-Segel equations based on a symmetrization reformation, which is equivalent to the convex splitting method and is free of any nonlinear solver. We show that, this new scheme is unconditionally…