An Adaptive Algorithm Based on Stochastic Discontinuous Galerkin for Convection Dominated Equations with Random Data
CoRR(2023)
摘要
In this paper, we propose an adaptive approach, based on mesh refinement or
parametric enrichment with polynomial degree adaption, for numerical solution
of convection dominated equations with random input data. A parametric system
emerged from an application of stochastic Galerkin approach is discretized by
using a symmetric interior penalty Galerkin (SIPG) method with upwinding for
the convection term in the spatial domain. We derive a residual-based error
estimator contributed by the error due to the SIPG discretization, the
(generalized) polynomial chaos discretization in the stochastic space, and data
oscillations. Then, the reliability of the proposed error estimator, an upper
bound for the energy error up to a multiplicative constant, is shown. Moreover,
to balance the errors stemmed from spatial and stochastic spaces, the
truncation error coming from Karhunen–Loève expansion is also considered
in the numerical simulations. Last, several benchmark examples including a
random diffusivity parameter, a random velocity parameter, random
diffusivity/velocity parameters, and a random (jump) discontinuous diffusivity
parameter, are tested to illustrate the performance of the proposed estimator.
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关键词
discontinuous galerkin,convection dominated equations,adaptive algorithm,stochastic
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