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cases,
in effectively
doubling nonlinear
of convergence with a local
negligible mesh. words, error
for linear
as well as some
uniform Key stability,
discontinuous estimate,
NASA/CR-2002-211959 ICASE Report No. 2002-42
Local Discontinuous Differential Equations
Shu
Galerkin
Methods
for Partial
with Higher
Order Derivatives
Jue Yan and Chi-Wang Brown University,
involving
discontinuous and
methods
for the
dependent fifth
bi-harmonic derivatives.
equations
involving
derivatives, correct
differential fluxes
equations and prove theseProvidence,
Rhode Island
November
2002
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Galerkin
method,
partial
differential
equations
with
higher
derivatives,
post-processing Applied In this paper partial and Numerical we review differential Mathematics and develop new local discontinuous order derivatives Galerkin meth-
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LOCAL
DISCONTINUOUS EQUATIONS
GALERKIN WITH
JUE
METHODS ORDER
CHI-WANG
FOR
PARTIAL
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new local discontinuous higher order derivatives
Galerkin in one
methods
dependent
differential discontinuous type
equations Galerkin
and multiple equations develop innew fourth
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TECHNICAL
MEMORANDUM.
Scientific and technical findings that are preliminary or of specialized interest, e.g., quick release reports, working papers, and bibliographies that contain minimal annotation. Does not contain extensive analysis.
DIFFERENTIAL
HIGHER
YAN f AND
DERIVATIVES*
SHU _
Abstract. for solving space volving local time
In this
paper
we review partial local
the existing
and
develop with
dimensions. second
We review derivatives Galerkin partial and
methods
for convection third derivatives. type For these
diffusion We then
for KdV
equations time
negative-order derivatives.
uous Galerkin technique with
with higher derivative cost,
Numerical
experiments the rate problems,
works
as well for the new higher additional computational
of
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TECHNICAL PUBLICATION. Reports completed research or a major significant phase of research that present the results of NASA programs and include extensive data or theoretical analysis. Includes compilations of significant scientific and technical data and information deemed to be of continuing reference counterpart of peer-reviewed professional papers, stringent limitations length and extent presentations.
Jue Yan and
Galerkin
Methods
for Partial
Equations
Shu
with Higher
Order Derivatives
Chi-Wang
Brown
University,