Related papers: An unstructured mesh control volume method for two…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construction principles of the methods, we review some literature…
An implicit Euler finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for the electron density matrix or, alternatively, of weakly…
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
This paper contains construction and analysis a finite element approximation for convection dominated diffusion problems with full coefficient matrix on general simplicial partitions in $R^d$, $d=2,3$. This construction is quite close to…
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…
We present a space-time extension of a conservative Cartesian cut-cell finite-volume method for two-phase diffusion problems with prescribed interface motion. The formulation follows a two-fluid approach: one scalar field is solved in each…
The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the maximal singular value of the stiffness…
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…
A simple but successful strategy for building a discrete diffusion operator in finite volume schemes of industrial use is to correct the standard two-point flux approximation with a term accounting for the local mesh non-orthogonality.…
We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous--discontinuous function…
In this paper, a novel meshless method that can handle porous flow problems with singular source terms is developed by virtually constructing the node control domains. By defining the connectable node cloud, this novel meshless method uses…
We introduce a new family of high order accurate semi-implicit schemes for the solution of non-linear hyperbolic partial differential equations on unstructured polygonal meshes. The time discretization is based on a splitting between…
In this manuscript we present a novel and efficient numerical method for the compressible viscous and resistive MHD equations for all Mach number regimes. The time-integration strategy is a semi-implicit splitting, combined with a hybrid…
We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…