Evolving Surface Finite Element Methods for Random Advection-Diffusion Equations

DOI10.1137/17M1149547zbMath1407.65258arXiv1702.07290MaRDI QIDQ4611531

Charles M. Elliott, Thomas Ranner, Ralf Kornhuber, Ana Djurdjevac

Publication date: 21 January 2019

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.07290

zbMATH Keywords

uncertainty quantificationsurface finite elementssurface PDEsrandom advection-diffusion equation

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (max. 100)

Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model ⋮ A domain mapping approach for elliptic equations posed on random bulk and surface domains ⋮ Uncertainty Quantification of Unsteady Flows Generated by Line-Sources Through Heterogeneous Geological Formations

Uses Software

• DUNE
• DUNE-FEM

Cites Work

• Unnamed Item
• Unnamed Item
• Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
• On some linear parabolic PDEs on moving hypersurfaces
• A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the DUNE-FEM module
• Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
• Isotropic Gaussian random fields on the sphere: regularity, fast simulation and stochastic partial differential equations
• A generic grid interface for parallel and adaptive scientific computing. I: Abstract framework
• A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in DUNE
• Numerical analysis of lognormal diffusions on the sphere
• Regularity properties and simulations of Gaussian random fields on the sphere cross time
• Advection-diffusion equations with random coefficients on evolving hypersurfaces
• The effect of growth and curvature on pattern formation
• Evolving surface finite element method for the Cahn-Hilliard equation
• An abstract framework for parabolic PDEs on evolving spaces
• Trace finite element methods for PDEs on surfaces
• Sparse Tensor Galerkin Discretization of Parametric and Random Parabolic PDEs---Analytic Regularity and Generalized Polynomial Chaos Approximation
• Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
• An Introduction to Computational Stochastic PDEs
• Numerical Analysis of the Advection-Diffusion of a Solute in Porous Media with Uncertainty
• Random Fields on the Sphere
• Tensor Spaces and Numerical Tensor Calculus
• Computation of geometric partial differential equations and mean curvature flow
• Finite elements on evolving surfaces
• Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
• Spectral Methods for Uncertainty Quantification
• Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients
• A Fully Discrete Evolving Surface Finite Element Method
• $L^2$-estimates for the evolving surface finite element method
• Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods
• Finite element methods for surface PDEs
• Variational discretization of wave equations on evolving surfaces
• Computer Vision - ECCV 2004
• Variational problems and partial differential equations on implicit surfaces
• Multigrid methods for discrete elliptic problems on triangular surfaces

This page was built for publication: Evolving Surface Finite Element Methods for Random Advection-Diffusion Equations