A stabilized finite element method for advection-diffusion equations on surfaces

2013/01/16 by Maxim A. Olshanskii, Olshanskii, Maxim A., Arnold Reusken +3 · 1 citation
Engineering · #58J32 #65N12 #65N30 #76D45 #76T99 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1301.3741

openalex publication_date 2013/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless the mesh is sufficiently fine. The paper introduces a stabilized finite element formulation based on the SUPG technique. An error analysis of the method is given. Results of numerical experiments are presented that illustrate the performance of the stabilized method.

Cited by

• A Finite Element framework for bulk-surface coupled PDEs to solve moving boundary problems in biophysics

Related

• A stabilized finite element formulation for advection-diffusion using the generalized finite element framework
• Stabilization with residual-free bubbles for advection-dominated transport equations
• A Stabilized Cut Streamline Diffusion Finite Element Method for Convection-Diffusion Problems on Surfaces
• MsFEM for advection-dominated problems in heterogeneous media: Stabilization via nonconforming variants
• Error analysis for an ALE evolving surface finite element method