Related papers: Structure preserving discretization method for 1D …
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 this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…
Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method…
We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements,…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
We present a novel structure-preserving semi-implicit finite volume method on vertex-based staggered meshes for the compatible discretization of first order systems of time-dependent partial differential equations (PDEs). The method…
In this paper, we develop high-order splitting methods for linear port-Hamiltonian systems, focusing on preserving their intrinsic structure, particularly the dissipation inequality. Port-Hamiltonian systems are characterized by their…
This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…
We study the numerical approximation of a class of degenerate parabolic stochastic partial differential equations on non-compact metric graphs, which naturally arise in the asymptotic analysis of Hamiltonian flows under small noise…
In this paper, we present and study discontinuous Galerkin (DG) methods for one-dimensional multi-symplectic Hamiltonian partial differential equations. We particularly focus on semi-discrete schemes with spatial discretization only, and…
We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is…
We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
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.…
This paper considers the numerical solution of Timoshenko beam network models, comprised of Timoshenko beam equations on each edge of the network, which are coupled at the nodes of the network using rigid joint conditions. Through…
In this article we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpoint of the discrete variational derivative method we propose…
A general framework for the numerical approximation of evolution problems is presented that allows to preserve exactly an underlying Hamiltonian- or gradient structure. The approach relies on rewriting the evolution problem in a particular…
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…
In this work we are interested in dealing with single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than…
We propose a two-dimensional asymptotic preserving scheme for linear transport equations with diffusive scalings. It is an extension of the time splitting developed by Jin, Pareschi and Toscani [SINUM,2000], but uses spatial discretizations…