Related papers: Unconditionally stable higher order semi-implicit …
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…
We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
We carry out a stability and convergence analysis of a fully discrete scheme for the time-dependent Navier-Stokes equations resulting from combining an $H(\mathrm{div}, \Omega)$-conforming discontinuous Galerkin spatial discretization, and…
We use the semi-discrete method, originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics, 89(6), to reproduce qualitative…
We develop and analyze a new hybridizable discontinuous Galerkin (HDG) method for solving third-order Korteweg-de Vries type equations. The approximate solutions are defined by a discrete version of a characterization of the exact solution…
Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…
A cell-centered implicit-explicit updated Lagrangian finite volume scheme on unstructured grids is proposed for a unified first order hyperbolic formulation of continuum fluid and solid mechanics. The scheme provably respects the stiff…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…
A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier--Stokes equations. The approach linearizes convection using an extrapolated (Oseen-type) convecting velocity, producing a…
This paper presents a novel and straightforward compact reconstruction procedure for the high-order finite volume method on unstructured grids. In this procedure, we constructed a linear approximation relationship between the mean values…
We investigate the properties of discretizations of advection equations on non-cartesian grids and graphs in general. Advection equations discretized on non-cartesian grids have remained a long-standing challenge as the structure of the…
We construct high-order semi-discrete-in-time and fully discrete (with Fourier-Galerkin in space) schemes for the incompressible Navier-Stokes equations with periodic boundary conditions, and carry out corresponding error analysis. The…
A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
A generalization of implicit conservative numerics to multiple dimensions requires advanced concepts of tensor analysis and differential geometry and hence a more thorough dedication to mathematical fundamentals than maybe expected at first…
The stability of classical semi-implicit scheme, and some more advanced iterative schemes recently proposed for Numerical Weather Prediction (NWP) purpose is examined. In all these schemes, the solution of the centred-implicit non-linear…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
This study aims to construct a stable, high-order compact finite difference method for solving Sobolev-type equations with Dirichlet boundary conditions in one-space dimension. Approximation of higher-order mixed derivatives in some…
We introduce a class of high order accurate, semi-implicit Runge-Kutta schemes in the general setting of evolution equations that arise as gradient flow for a cost function, possibly with respect to an inner product that depends on the…