A narrow-band unfitted finite element method for elliptic PDEs posed on surfaces

DOI10.1090/mcom/3030zbMath1335.65094arXiv1401.7697OpenAlexW2592754172MaRDI QIDQ2796011

D. Safin, Maxim A. Olshanskii

Publication date: 23 March 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.7697

zbMATH Keywords

surfaceconvergencenumerical examplefinite element methoderror analysislevel set methodelliptic equation

Mathematics Subject Classification ID

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) Elliptic equations on manifolds, general theory (58J05)

Related Items (13)

Numerical modeling of phase separation on dynamic surfaces ⋮ A trace finite element method for a class of coupled bulk-interface transport problems ⋮ Analysis of the finite element method for the Laplace-Beltrami equation on surfaces with regions of high curvature using graded meshes ⋮ Numerical integration over implicitly defined domains for higher order unfitted finite element methods ⋮ A hybrid finite volume -- finite element method for bulk-surface coupled problems ⋮ Curvature-Driven Molecular Flow on Membrane Surface ⋮ Parametric Polynomial Preserving Recovery on Manifolds ⋮ Surface Crouzeix-Raviart element for the Laplace-Beltrami equation ⋮ A flux-corrected RBF-FD method for convection dominated problems in domains and on manifolds ⋮ An Eulerian finite element method for PDEs in time-dependent domains ⋮ Volumetric variational principles for a class of partial differential equations defined on surfaces and curves ⋮ Time-Periodic Solutions of Advection-Diffusion Equations on Moving Hypersurfaces ⋮ An AFC-stabilized implicit finite element method for partial differential equations on evolving-in-time surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A finite element method for surface PDEs: Matrix properties
• An improvement of a recent Eulerian method for solving PDEs on general geometries
• Modeling and computation of two phase geometric biomembranes using surface finite elements
• Finite element approximation of elliptic partial differential equations on implicit surfaces
• An Eulerian formulation for solving partial differential equations along a moving interface
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• Highly accurate surface and volume integration on implicit domains by means of moment-fitting
• A Finite Element Method for Elliptic Equations on Surfaces
• Numerical Methods for Two-phase Incompressible Flows
• Shorter Notes: Regularity of the Distance Function
• An h-narrow band finite-element method for elliptic equations on implicit surfaces
• Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
• Numerical comparison of some Hessian recovery techniques
• A Finite-element Method for Solving Elliptic Equations with Neumann Data on a Curved Boundary Using Unfitted Meshes
• Iterative Solution Methods
• On a discrete Hessian recovery for P 1 finite elements
• Finite element analysis for a coupled bulk-surface partial differential equation
• Non-degenerate Eulerian finite element method for solving PDEs on surfaces
• Finite element methods for surface PDEs
• An Adaptive Finite Element Method for the Laplace–Beltrami Operator on Implicitly Defined Surfaces
• Variational problems and partial differential equations on implicit surfaces

This page was built for publication: A narrow-band unfitted finite element method for elliptic PDEs posed on surfaces