On a finite element method for three‐dimensional unsteady compressible viscous flows

Abstract

In this article we analyze a finite element method for three-dimensional unsteady compressible NavierStokes equations. We prove the existence and uniqueness of the numerical solution, and obtain a priori error estimates uniform in time. Numerical computations are carried out to test the orders of accuracy in the error estimates. Blend function interpolations are applied in the calculation of numerical integrations.

Air pollution modelling using a Graphics Processing Unit with CUDA

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“…Here the partial differential equations describing the variation of the concentrations of species over time can be solved with various numerical methods (e.g. Finite Element Method, Method of Lines, etc) [1][2][3][4]. The basis of the Method of Lines is the spatial discretisation of partial differential equations followed by time integration of produced ordinary differential equations with appropriate initial and boundary conditions.…”

Unconditional convergence and error estimates for bounded numerical solutions of the barotropic Navier–Stokes system

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The analysis of a finite element method for the three-species Lotka–Volterra competition-diffusion with Dirichlet boundary conditions

“…We start by working with a similar procedure to Liu's [13,14] for the case of compressible Navier-Stokes flow problems. We assume that the initial conditions by choosing A 0 i,h as the Ritz projection of A 0 i onto the FE subspace V h to the numerical algorithm (8) is considered.…”