No abstract

Transformation of dependent variables as, for example, the Kirchhoff transformation, is a classical tool for solving nonlinear partial differential equations. This approach is used here in connection with the finite element method and explained first in case of nonlinear heat conduction problems without phase change. The main applications of the method given in the paper concern a nonlinear degenerate parabolic equation for fluid flow through a porous medium and Stefan (moving boundary) problems.

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The purpose of this article is to demonstrate that the discontinuous Galerkin method is efficient and suitable to solve linearized Euler equations, modelling sound propagation phenomena. Several benchmark problems were chosen for this purpose. We studied the effect of the underlying computational mesh on the convergence rate and showed the importance of high-quality meshes in order to achieve the theoretical convergence rates. Various acoustic boundary conditions were examined. Perfectly matched layer was used as a non-reflecting boundary condition.

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.