A non-overlapping domain decomposition method for parabolic initial-boundary value problems

A non-overlapping domain decomposition method with adaptive interface conditions is applied to parabolic initial-boundary value problems in the full range from diffusion- to advection-dominated problems. The basic discretizations are the discontinuous Galerkin method in time and a stabilized Galerki...

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Bibliographic Details
Published in:Applied numerical mathematics Vol. 28; no. 2; pp. 359 - 369
Main Authors: Lube, G., Otto, F.C., Müller, H.
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 01.10.1998
Elsevier
Subjects:
Advection-reaction-diffusion
Exact sciences and technology
Mathematics
Non-overlapping domain decomposition method
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Advection-reaction-diffusion
Non-overlapping domain decomposition method
Grid pattern
Initial value problem
Advection diffusion equation
Numerical method
Partial differential equation
Discretization method
Galerkin-Petrov method
Parabolic equation
Elliptic equation
Boundary value problem
Convergence rate
Domain decomposition
Numerical convergence
ISSN:0168-9274, 1873-5460
Online Access:Get full text
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Summary:A non-overlapping domain decomposition method with adaptive interface conditions is applied to parabolic initial-boundary value problems in the full range from diffusion- to advection-dominated problems. The basic discretizations are the discontinuous Galerkin method in time and a stabilized Galerkin method in space. A convergence proof is available in appropriate Sobolev norms for the continuous elliptic problems arising in each time step. The numerical convergence rate is independent of the mesh size. Finally we extend the approach to more complex problems.
ISSN:0168-9274
1873-5460
DOI:10.1016/S0168-9274(98)00053-1