A continuous finite element method to approximate Friedrichs' systems is proposed and analyzed. Stability is achieved by penalizing the jumps across mesh interfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal of order ½ convergence rates in the L2-norm. A variant of the method specialized to Friedrichs' systems associated with elliptic PDE's in mixed form and reducing the number...

In this article we introduce an adaptive multi-level method in space and time for convection diffusion problems. The scheme is based on a multi-level spatial splitting and the use of different time-steps. The temporal discretization relies on the characteristics method. We derive an a posteriori error estimate and design a corresponding adaptive algorithm. The efficiency of the multi-level method is illustrated by numerical experiments, in particular for a convection-dominated problem.

We present the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume barycentric mesh, whereas the diffusion term is discretized by piecewise linear nonconforming triangular finite elements. Under the assumption that the triangulations are of weakly...

We consider the double-diffusive convection phenomenon and analyze the governing equations. A system of partial differential equations describing the convective flow arising when a layer of fluid with a dissolved solute is heated from below is considered. The problem is placed in a functional analytic setting in order to prove a theorem on existence, uniqueness and continuous dependence on initial data of weak solutions in the class $([0,\infty );H)\cap L{²}_{loc}({ℝ}^{+};V)$. This theorem enables us to show that the infinite-dimensional...