DOMAIN DECOMPOSITION TYPE ITERATIVE TECHNIQUES FOR PARABOLIC PROBLEMS ON LOCALLY REFINED GRIDS Academic Article

abstract

• Based on an extension of the discontinuous Galerkin finite element method, discretization schemes for solving parabolic problems on grids with local refinement, both in space and in time, are constructed. The stability of schemes constructed in this way is automatically ensured by the method. The construction of two-level preconditioners utilizing local timestepping and a global coarse-grid solver both on standard, rectangular, and uniform grids, is the main objective of the paper. The optimal convergence properties of such two-level preconditioners are studied. The theory is illustrated by a set of numerical examples.

authors

• Lazarov, Raytcho
• Pasciak, Joseph

published proceedings

• SIAM JOURNAL ON NUMERICAL ANALYSIS

author list (cited authors)

• EWING, R. E., LAZAROV, R. D., PASCIAK, J. E., & VASSILEVSKI, P. S.

citation count

• 13

complete list of authors

• EWING, RE||LAZAROV, RD||PASCIAK, JE||VASSILEVSKI, PS

publication date

• January 1993

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• 2-level Method
• Discontinuous Galerkin Method
• Domain Decomposition
• Generalized Conjugate Gradient Method
• Local Refinement
• Optimal-order Preconditioner
• Parabolic Problem

Digital Object Identifier (DOI)

• 10.1137/0730080

start page

• 1537

end page

• 1557

volume

• 30

issue

• 6

URL

• http://dx.doi.org/10.1137/0730080