Microstructural evolution in inhomogeneous elastic media
Journal of Computational Physics
The immersed interface method using a finite element formulation
Applied Numerical Mathematics
The immersed finite volume element methods for the elliptic interface problems
Mathematics and Computers in Simulation - Special issue from IMACS sponsored conference: “Modelling '98”
Microstructural evolution in orthotropic elastic media
Journal of Computational Physics
A p-th degree immersed finite element for boundary value problems with discontinuous coefficients
Applied Numerical Mathematics
A Trilinear Immersed Finite Element Method for Solving the Electroencephalography Forward Problem
SIAM Journal on Scientific Computing
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This article is to discuss the linear (which was proposed in [18,19]) and bilinear immersed finite element (IFE) methods for solving planar elasticity interface problems with structured Cartesian meshes. Basic features of linear and bilinear IFE functions, including the unisolvent property, will be discussed. While both methods have comparable accuracy, the bilinear IFE method requires less time for assembling its algebraic system. Our analysis further indicates that the bilinear IFE functions are guaranteed to be applicable to a larger class of elasticity interface problems than linear IFE functions. Numerical examples are provided to demonstrate that both linear and bilinear IFE spaces have the optimal approximation capability, and that numerical solutions produced by a Galerkin method with these IFE functions for elasticity interface problem also converge optimally in both L^2 and semi-H^1 norms.