Related papers: Structure-preserving Discretization of the Hessian…
In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward…
In this article we apply a discrete action principle for the Vlasov--Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the finite-dimensional electromagnetic potentials and fields are…
In this paper we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the…
We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…
This work proposes a new approach to study transport properties of highly correlated local structures. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster…
This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and…
In this paper, we introduce second order and fourth order space discretization via finite difference implementation of the finite element method for solving Fokker-Planck equations associated with irreversible processes. The proposed…
We propose a novel formulation for parametric finite element methods to simulate surface diffusion of closed curves, which is also called as the curve diffusion. Several high-order temporal discretizations are proposed based on this new…
We introduce meshfree finite difference methods for approximating nonlinear elliptic operators that depend on second directional derivatives or the eigenvalues of the Hessian. Approximations are defined on unstructured point clouds, which…
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial…
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 rigorous, conservative invariant-domain preserving (IDP) projection technique for hierarchical discretizations that enforces membership in physics-implied convex sets when mapping between solution spaces. When coupled with…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
In the present work we calculate the group structure of the Schlesinger transformations for isomonodromic deformations of order two Fuchsian differential equations. We perform these transformations as the isomorphisms between the moduli…
This chapter provides an introduction to Hybrid High-Order (HHO) methods. These are new generation numerical methods for PDEs with several advantageous features: the support of arbitrary approximation orders on general polyhedral meshes,…
Isogeometric Analysis (IGA) is a computational technique for the numerical approximation of partial differential equations (PDEs). This technique is based on the use of spline-type basis functions, that are able to hold a global smoothness…
We study in this paper a multilayer discretization of second order elliptic problems, aimed at providing reliable multilayer discretizations of shallow fluid flow problems with diffusive effects. This discretization is based upon the…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
We propose and analyze a structure-preserving space-time variational discretization method for the Cahn-Hilliard-Navier-Stokes system. Uniqueness and stability for the discrete problem is established in the presence of concentration…