Evolving surface finite element methods for random advection-diffusion\n equations

2017/02/23 by Ana Djurdjevac, Charles M. Elliott, Djurdjevac, Ana +5 · 1 citation
Computer Science · Decision Sciences · Engineering · #65C05 #65N12 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1702.07290

openalex publication_date 2017/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce and analyse a surface finite element\ndiscretization of advection-diffusion equations with uncertain coefficients on\nevolving hypersurfaces. After stating unique solvability of the resulting\nsemi-discrete problem, we prove optimal error bounds for the semi-discrete\nsolution and Monte Carlo samplings of its expectation in appropriate Bochner\nspaces. Our theoretical findings are illustrated by numerical experiments in\ntwo and three space dimensions.\n

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