×

The heterogeneous multiscale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems. (English) Zbl 1080.65090

Summary: We develop a discontinuous Galerkin method, within the framework of the heterogeneous multiscale method, for solving hyperbolic and parabolic multiscale problems. Hyperbolic scalar equations and systems, as well as parabolic scalar problems, are considered. Error estimates are given for the linear equations, and numerical results are provided for the linear and nonlinear problems to demonstrate the capability of the method.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35L45 Initial value problems for first-order hyperbolic systems
35K15 Initial value problems for second-order parabolic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI