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This paper deals with a time-domain mathematical model for dissipative acoustics and is organized as follows. First, the equations of this model are written in terms of displacement and temperature fields and an energy equation is obtained. The resulting initial-boundary value problem is written in a functional framework allowing us to prove the existence and uniqueness of solution. Next, two different time-discretization schemes are proposed, and stability and error estimates are proved for both. Finally, numerical results are reported which were obtained by combining these time-schemes with Lagrangian and Raviart–Thomas finite elements for temperature and displacement fields, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we consider a 1D inviscid model to simulate river flows whose unknown are the water elevation, the flow rate and the wet area. We rewrite this model in terms of the wet area and the flow rate. Next, by using a weak formulation and a discretization by characteristics, we derive an implicit semidiscretized scheme that involves a variational inequality. Under suitable hypothesis, we prove that this scheme has at least one solution. We present an algorithm for the numerical solution of the fully discretized problem and the numerical results obtained for channels with parabolic and rectangular sections and variable depth. Finally, we perform a stability analysis for the semidiscretized scheme applied to a similar problem where the convection term has been omitted. [ABSTRACT FROM AUTHOR]

In this paper we analyze the Residual-Free Bubble (RFB) method applied to the linear diffusion­advection­reaction problem. We propose a new a priori error analysis for the method and for its practical implementation in a quite general context, which allows, e.g. linear or quadratic elements on the resolvable scales. We also perform some numerical tests, showing in both cases the advantages of the method. [ABSTRACT FROM AUTHOR]