Related papers: Mimetic Spectral Element advection
We study a symmetric BEM-FEM coupling scheme for the scattering of transient acoustic waves by bounded inhomogeneous anisotropic obstacles in a homogeneous field. An incident wave in free space interacts with the obstacles and produces a…
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…
Compatible discretizations, such as finite element exterior calculus, provide a discretization framework that respect the cohomological structure of the de Rham complex, which can be used to systematically construct stable mixed finite…
This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and…
A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…
We present a procedure for the systematic estimation of the dispersion properties of linear discrete systems with periodic time-varying coefficients. The approach relies on the analysis of a single unit cell, making use of Bloch theorem…
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
This work considers to numerically solve a subdiffusion equation involving constant time delay $\tau$ and Riemann-Liouville fractional derivative. First, a fully discrete finite element scheme is developed for the considered problem under…
We present an improved analysis of the Euler-Maruyama discretization of the Langevin diffusion. Our analysis does not require global contractivity, and yields polynomial dependence on the time horizon. Compared to existing approaches, we…
In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the $d$-dimensional advection-diffusion equation, our proposal is a two-level algorithm…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
This paper studies the spectral properties of large matrices and the preconditioning of linear systems, arising from the finite difference discretization of a time-dependent space-fractional diffusion equation with a variable coefficient…
We present a novel approach that redefines the traditional interpretation of explicit and implicit discretization methods for solving a general class of advection-diffusion equations (ADEs) featuring nonlinear advection, diffusion…
Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
We develop an analytic perturbation theory for eigenvalues with finite multiplicities, embedded into the essential spectrum of a self-adjoint operator $H$. We assume the existence of another self-adjoint operator $A$ for which the family…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
We comment on the discretization of the Dirac equation using finite element spaces of differential forms. In order to treat perturbations by low order terms, such as those arizing from electromagnetic fields, we develop some abstract…