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An EMC-HDG scheme for the convection-diffusion equation with random diffusivity

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Abstract

In this work, we propose an ensemble Monte Carlo hybridizable discontinuous Galerkin (EMC-HDG) algorithm to simulate the convection-diffusion equation with random diffusion coefficients. The EMC-HDG algorithm reduces the computation cost compared with Monte Carlo HDG (MC-HDG) method. This algorithm is a semi-implicit scheme which shares a common coefficient matrix with multiple right-hand-vectors by introducing an ensemble average of coefficient functions. Moreover, for the numerical approximation, optimal convergence rate O(hk+ 1) in space and O(△t) in time are obtained. To confirm our theoretical results, several numerical experiments are also presented.

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Funding

This work is supported by NSF of China (No. 11961008), talent introduction fund of Guizhou University ([2013] No. 53).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guizhou University, 2708 South Huaxi Avenue, Guiyang, 550025, Guizhou, China

    Meng Li & Xianbing Luo

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  1. Meng Li
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  2. Xianbing Luo
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Correspondence to Xianbing Luo.

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Li, M., Luo, X. An EMC-HDG scheme for the convection-diffusion equation with random diffusivity. Numer Algor 90, 1755–1776 (2022). https://doi.org/10.1007/s11075-021-01250-2

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