Browsing by Author "Lamač, Jan"
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- ItemAnalysis and application of the discontinuous Galerkin method to the RLW equation(Springer International Publishing Ag, 2013) Hozman, Jiří; Lamač, JanIn this work, our main purpose is to develop of a sufficiently robust, accurate and efficient numerical scheme for the solution of the regularized long wave (RLW) equation, an important partial differential equation with quadratic nonlinearity, describing a large number of physical phenomena. The crucial idea is based on the discretization of the RLW equation with the aid of a combination of the discontinuous Galerkin method for the space semi-discretization and the backward difference formula for the time discretization. Furthermore, a suitable linearization preserves a linear algebraic problem at each time level. We present error analysis of the proposed scheme for the case of nonsymmetric discretization of the dispersive term. The appended numerical experiments confirm theoretical results and investigate the conservative properties of the RLW equation related to mass, momentum and energy. Both procedures illustrate the potency of the scheme consequently.
- ItemNumerical solution of reaction-diffusion equations(Technická univerzita v Liberci, Česká republika, 2012) Lamač, JanThe subject of the presented paper is a mathematical analysis and numerical solution of the sys- tem of nonlinear nonstationary reaction-diffusion equations. Firstly, using the invariant region technique, the proof of both the existence and uniqueness of the solution and problem data con- tinuous dependence is carried out. After time discretization of the problem the Galerkin finite elements method is applied and a priori error estimates of the method are derived. A suitable mesh adaptivity is discussed as well. The method is finally implemented and tested on several examples.