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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Multigrid solution of monotone second-order discretizations of hyperbolic conservation laws
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by Stefan Spekreijse PDF
Math. Comp. 49 (1987), 135-155 Request permission

Abstract:

This paper is concerned with two subjects: the construction of second-order accurate monotone upwind schemes for hyperbolic conservation laws and the multigrid solution of the resulting discrete steady-state equations. By the use of an appropriate definition of monotonicity, it is shown that there is no conflict between second-order accuracy and monotonicity (neither in one nor in more dimensions). It is shown that a symmetric block Gauss-Seidel underrelaxation (each block is associated with 4 cells) has satisfactory smoothing rates. The success of this relaxation is due to the fact that, by coupling the unknowns in such blocks, the nine-point stencil of a second-order 2D upwind discretization changes into a five-point block stencil.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 135-155
  • MSC: Primary 65N05; Secondary 35L65, 76G15
  • DOI: https://doi.org/10.1090/S0025-5718-1987-0890258-9
  • MathSciNet review: 890258