Search

The solution of the singular perturbation problems (SPP) of convection-diffusion-reaction type may exhibit regular and corner layers in a rectangular domain. In this work, we construct and analyze a parameter-uniform operator-splitting alternating direction implicit (ADI) scheme to efficiently solve a two-dimensional parabolic singularly perturbed problem with two positive parameters. The proposed model is a combination of the backward-Euler method defined on a uniform mesh in time and a hybrid method in space defined on a special Shishkin mesh. The analysis is presented on a layer adapted piecewise-uniform Shishkin mesh. The developed numerical method is proved to be first-order convergent in time and almost second-order convergent in space. The numerical experiments are performed to validate the theoretical convergence results and illustrate the efficiency of the current strategy. [ABSTRACT FROM AUTHOR]

• The governing equations are a system of five coupled convection-diffusion-reaction equations. • Error estimates are obtained using residuals due to space discretization, time discretization and linearization. • Fully computable a posteriori error estimates are derived using the total residual. • An adaptive finite element solution of these model equations is computed and the performance is illustrated. The a posteriori error estimates for finite element approximations to the governing equations of heat and mass transfer in fluidized beds are derived in this work. These are a system of five time dependent coupled nonlinear convection-diffusion-reaction equations. Based on the variational formulation, computable residual based a posteriori error estimates are obtained. The time discretization has been done using the implicit Euler method. The a posteriori error estimates for all the five variables are derived using the total residual and error indicators due to spatial discretization, time discretization and linearization. An adaptive finite element solution of these model equations is computed and the performance is illustrated. [ABSTRACT FROM AUTHOR]

• The governing equations are five coupled semilinear convection-diffusion-reaction equations. • DG method is used to find the numerical solution which is well suited for convection dominated problems. • Experimental order of convergence of two and three are achieved. • DG methods are easily parallelizable. Parallel efficiency of strong scaling is presented. • A priori error estimates of DG method for all the five primary variables are derived. In this work, the Discontinuous Galerkin (DG) schemes were studied for the solution of convection-diffusion-reaction equations which arise from mathematical modeling of fluidized bed spray granulation process (FBSG). The discontinuous Galerkin method for space discretization is employed to treat the dominated convection behavior in the governing equations. The implicit Euler method for the temporal discretization is used. The mathematical analysis of the governing equations with a priori bounds for all the state variables is demonstrated. The investigation of experimental order of convergence is presented for test functions of degrees one and two. Finally, parallel efficiency of strong scaling is presented for the employed DG schemes. [ABSTRACT FROM AUTHOR]