TY - JOUR
T1 - Variational structure of the optimal artificial diffusion method for the advectiondiffusion equation
AU - Nakshatrala, K. B.
AU - Valocchi, A. J.
N1 - Funding Information:
Nakshatrala acknowledges the financial support given by the Texas Engineering Experiment Station (TEES). Valocchi was supported by the Department of Energy through a SciDAC-2 project (Grant No. DOE DE-FCO207ER64323). The opinions expressed in this paper are those of the authors and do not necessarily reflect that of the sponsors.
PY - 2010/12
Y1 - 2010/12
N2 - In this research note, we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions when applied to one-dimensional (1D) problems with constant coefficients and forcing function. We first present a variational principle for a multi-dimensional advective-diffusive system, and then derive a new stable weak formulation. When applied to 1D problems with constant coefficients and forcing function, this resulting weak formulation will be equivalent to the optimal artificial diffusion method. We present representative numerical results to corroborate our theoretical findings.
AB - In this research note, we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions when applied to one-dimensional (1D) problems with constant coefficients and forcing function. We first present a variational principle for a multi-dimensional advective-diffusive system, and then derive a new stable weak formulation. When applied to 1D problems with constant coefficients and forcing function, this resulting weak formulation will be equivalent to the optimal artificial diffusion method. We present representative numerical results to corroborate our theoretical findings.
KW - EulerLagrange equations
KW - Variational principles
KW - advectiondiffusion equation
KW - optimal artificial diffusion
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U2 - 10.1142/S0219876210002350
DO - 10.1142/S0219876210002350
M3 - Article
AN - SCOPUS:79551675250
SN - 0219-8762
VL - 7
SP - 559
EP - 572
JO - International Journal of Computational Methods
JF - International Journal of Computational Methods
IS - 4
ER -