Related papers: Compatible finite element methods for geophysical …
$L^2$ norm error estimates of semi- and full discretisations, using bulk--surface finite elements and Runge--Kutta methods, of wave equations with dynamic boundary conditions are studied. The analysis resides on an abstract formulation and…
In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely…
Hydrodynamical simulations are the most accurate way to model structure formation in the universe, but they often involve a large number of astrophysical parameters modeling subgrid physics, in addition to cosmological parameters. This…
Numerical models of weather and climate critically depend on long-term stability of integrators for systems of hyperbolic conservation laws. While such stability is often obtained from (physical or numerical) dissipation terms, physical…
Within the finite element community, discontinuous Galerkin (DG) and mixed finite element methods have become increasingly popular in simulating geophysical flows. However, robust and efficient solvers for the resulting saddle-point and…
Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial…
We present the implementation of a solution scheme for fluid-structure interaction problems via the finite element software library deal.II. The solution scheme is an immersed finite element method in which two independent discretizations…
This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…
A finite element model and its equivalent electronic analogue circuit of hydraulic transmission lines have been developed. Basic equations are approximated to be a set of ordinary differential equations that can be represented in state…
A vertical slice model is developed for the Euler-Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady-Boussinesq model). The model is a solution of the full three-dimensional equations…
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…
Thanks to modern manufacturing technologies, heterogeneous materials with complex inner structures (e.g., foams) can be easily produced. However, their utilization is not straightforward, as the classical constitutive laws are not…
The present paper studies finite element discretizations of second-order elliptic boundary value problems with homogeneous right-hand side and inhomogeneous boundary conditions. We establish discrete spatial decay estimates on element…
This paper presents a family of spatial discretisations of the nonlinear rotating shallow-water equations that conserve both energy and potential enstrophy. These are based on two-dimensional mixed finite element methods and hence, unlike…
In this paper, a class of finite difference numerical techniques is presented to solve the second-order linear inhomogeneous damped wave equation. The consistency, stability, and convergences of these numerical schemes are discussed. The…
In this paper we proposed a two-level finite element discretization of the nonlinear stationary quasi-geostrophic equations, which model the wind driven large scale ocean circulation. Optimal error estimates for the two-level finite element…
A nonhydrostatic dynamical core has been developed by using the multi-moment finite volume method that ensures the rigorous numerical conservation. To represent the spherical geometry free of polar problems, the cubed-sphere grid is…
This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…
This article introduces a novel approach for broken-FEEC (Finite Element Exterior Calculus), extending its application to locally refined spline spaces with non-matching interfaces. Traditional broken-FEEC allows for discontinuous…
A hydraulic fracturing system with super-hydrophobic proppants is characterized by a transient triple-porosity Navier-Stokes model. For this complex multiphysics system, particularly in the context of three-dimensional space, a local…