Related papers: Implicit finite difference schemes for the magneti…
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…
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.…
In this work, we explore various relevant aspects of the Smoothed Particle Hydrodynamics regarding Burger's equation. The stability, precision, and efficiency of the algorithm are investigated in terms of different implementations. In…
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.…
Differential equations arising in fluid mechanics are usually derived from the intrinsic properties of mechanical systems, in the form of conservation laws, and bear symmetries, which are not generally preserved by a finite difference…
In wave propagation problems, finite difference methods implemented on staggered grids are commonly used to avoid checkerboard patterns and to improve accuracy in the approximation of short-wavelength components of the solutions. In this…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation, while building…
In theory, boundary and initial conditions are important for the wellposedness of partial differential equations (PDEs). Numerically, these conditions can be enforced exactly in classical numerical methods, such as finite difference method…
The construction of stable, conservative, and accurate volume dissipation is extended to discretizations that possess a generalized summation-by-parts (SBP) property within a tensor-product framework. The dissipation operators can be…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential…
We discuss finite difference techniques for hyperbolic equations in non-trivial domains, as those that arise when simulating black hole spacetimes. In particular, we construct dissipative and difference operators that satisfy the {\it…
In this paper we introduce a procedure, based on the method of equivariant moving frames, for formulating continuous Galerkin finite element schemes that preserve the Lie point symmetries of initial value problems for ordinary differential…
A new integration scheme, combining the stability and the precision of usual pseudo-spectral codes with the locality of finite differences methods, is introduced. It turns out to be particularly suitable for the study of front and…
Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational…
We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction that are applicable in level set methods. The most involved…
We apply a composite idea of semi-discrete finite difference approximation in time and Galerkin finite element method in space to solve the Navier-Stokes equations with Caputo derivative of order 0 < {\alpha} < 1. The stability properties…
In this paper, we show that diagonal-norm summation by parts (SBP) discretizations of general non-conservative systems of hyperbolic balance laws can be rewritten as a finite-volume-type formula, also known as flux-differencing formula, if…
A fast and stable numerical method is formulated to compute the time evolution of a wave function in a magnetic field by solving the time-dependent Schroedinger equation. This computational method is based on the finite element method in…