Numerical integration over implicitly defined domains for higher order unfitted finite element methods

DOI10.1134/S1995080216050103zbMath1354.65252arXiv1601.06182OpenAlexW2963374633MaRDI QIDQ345340

D. Safin, Maxim A. Olshanskii

Publication date: 1 December 2016

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

Full work available at URL: https://arxiv.org/abs/1601.06182

zbMATH Keywords

numerical integrationnumerical examplessubdivisionlevel set methodPoisson equationmoment-fittingMonte Carlo techniquesnumerical complexityunfitted finite element methods

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Monte Carlo methods (65C05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Complexity and performance of numerical algorithms (65Y20)

Related Items (16)

Numerical modeling of phase separation on dynamic surfaces ⋮ A finite element method for two-phase flow with material viscous interface ⋮ The high-order shifted boundary method and its analysis ⋮ A Stabilized Trace Finite Element Method for Partial Differential Equations on Evolving Surfaces ⋮ Adaptive quadrature/cubature rule: application to polytopes ⋮ Approximate integrals over bounded volumes with smooth boundaries ⋮ Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems ⋮ A high-order source removal finite element method for a class of elliptic interface problems ⋮ A Consistent Analytical Formulation for Volume Estimation of Geometries Enclosed by Implicitly Defined Surfaces ⋮ Numerical integration over implicitly defined domains with topological guarantee ⋮ A \(C^1\)-continuous trace-finite-cell-method for linear thin shell analysis on implicitly defined surfaces ⋮ Higher-order meshing of implicit geometries. II: Approximations on manifolds ⋮ An Eulerian finite element method for PDEs in time-dependent domains ⋮ A characterization for the validity of the Hermite-Hadamard inequality on a simplex ⋮ An unfitted finite element method for the Darcy problem in a fracture network ⋮ Using High-Order Transport Theorems for Implicitly Defined Moving Curves to Perform Quadrature on Planar Domains

Uses Software

• CutFEM

Cites Work

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