Related papers: Fully-discrete provably Lyapunov consistent discre…
Finite difference/element/volume methods of discretising PDEs impose a subgrid scale interpolation on the dynamics. In contrast, the holistic discretisation approach developed herein constructs a natural subgrid scale field adapted to the…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
Discrete diffusion models have gained increasing attention for their ability to model complex distributions with tractable sampling and inference. However, the error analysis for discrete diffusion models remains less well-understood. In…
Algebraically stabilized finite element discretizations of scalar steady-state convection-diffusion-reaction equations often provide accurate approximate solutions satisfying the discrete maximum principle (DMP). However, it was observed…
The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the under-resolved regime, mass conservation as well as energy stability…
We are interested in the large-time behavior of solutions to finite volume discretizations of convection-diffusion equations or systems endowed with non-homogeneous Dirichlet and Neumann type boundary conditions. Our results concern various…
We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which employs a semi-Lagrangian approach to approximate in time both the advective and the diffusive…
We develop unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad \mathbb{R}^N\times(0,T), $$…
We consider a model convection-diffusion problem and present useful connections between the finite differences and finite element discretization methods. We introduce a general upwinding Petrov-Galerkin discretization based on bubble…
We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…
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…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Although the spatially continuous version of the reaction-diffusion equation has been well studied, in some instances a spatially-discretized representation provides a more realistic approximation of biological processes. Indeed,…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
This work presents the discontinuous Galerkin discretization of the consistent splitting scheme proposed by Liu [J. Liu, J. Comp. Phys., 228(19), 2009]. The method enforces the divergence-free constraint implicitly, removing…
We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard finite element…
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…