Immersed finite element methods for 4th order differential equations

DOI10.1016/j.cam.2011.01.041zbMath1219.65135OpenAlexW2057460380MaRDI QIDQ544234

Zhu Wang, Yan Ping Lin, Sun, Weiwei, Tao Lin

Publication date: 14 June 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.01.041

zbMATH Keywords

numerical examplesdiscontinuous coefficientsinterface problemimmersed finite element methodfourth order boundary value problems

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with low regular coefficients and/or low regular data (35R05) Linear ordinary differential equations and systems (34A30) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (16)

An efficient meshfree point collocation moving least squares method to solve the interface problems with nonhomogeneous jump conditions ⋮ Long time error estimates of IFE methods for the unsteady multi-layer porous wall model ⋮ An augmented method for 4th order PDEs with discontinuous coefficients ⋮ A unified immersed finite element error analysis for one-dimensional interface problems ⋮ An Arbitrary Order Reconstructed Discontinuous Approximation to Biharmonic Interface Problem ⋮ Higher order numerical discretizations for exterior and biharmonic type PDEs ⋮ Higher degree immersed finite element spaces constructed according to the actual interface ⋮ A Nitsche extended finite element method for the biharmonic interface problem ⋮ A selective immersed discontinuous Galerkin method for elliptic interface problems ⋮ Unnamed Item ⋮ A 3D immersed finite element method with non-homogeneous interface flux jump for applications in particle-in-cell simulations of plasma-lunar surface interactions ⋮ Discontinuous Galerkin immersed finite element methods for parabolic interface problems ⋮ A family of two-grid partially penalized immersed finite element methods for semi-linear parabolic interface problems ⋮ A Nitsche mixed extended finite element method for the biharmonic interface problem ⋮ Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems ⋮ A generalized finite difference method for solving biharmonic interface problems

Cites Work

• A finite element method for interface problems in domains with smooth boundaries and interfaces
• Composite finite elements for elliptic boundary value problems with discontinuous coefficients
• A \(p\)-th degree immersed finite element for boundary value problems with discontinuous coefficients
• The immersed interface method using a finite element formulation
• Finite element methods and their convergence for elliptic and parabolic interface problems
• New Cartesian grid methods for interface problems using the finite element formulation
• Quadratic immersed finite element spaces and their approximation capabilities
• The finite element method for elliptic equations with discontinuous coefficients
• Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods
• Three-dimensional immersed finite element methods for electric field simulation in composite materials
• Approximation capability of a bilinear immersed finite element space
• A mixed method for 4th order problems using linear finite elements
• An immersed finite element space and its approximation capability
• Can a finite element method perform arbitrarily badly?
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Immersed finite element methods for 4th order differential equations