Superconvergence of Immersed Finite Volume Methods for One-Dimensional Interface Problems
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DOI: 10.1007/s10915-017-0532-6
Abstract: In this paper, we introduce a class of high order immersed finite volume methods (IFVM) for one-dimensional interface problems. We show the optimal convergence of IFVM in $$H^1$$H1- and $$L^2$$L2-norms. We also prove some superconvergence… read more here.
Keywords: immersed finite; volume methods; interface problems; finite volume ... See more keywords
A Rigorous Condition Number Estimate of an Immersed Finite Element Method
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DOI: 10.1007/s10915-020-01212-1
Abstract: It is known that the convergence rate of the traditional iteration methods like the conjugate gradient method depends on the condition number of the stiffness matrix. Moreover the construction of fast solvers like multigrid and… read more here.
Keywords: immersed finite; rigorous condition; condition; number estimate ... See more keywords
Nonconforming immersed finite element method for solving elliptic optimal control problems with interfaces
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DOI: 10.1080/00036811.2020.1802431
Abstract: In this paper, we present a nonconforming immersed finite element method for solving elliptic optimal control problems with interfaces. The immersed finite element space is constructed based on the... read more here.
Keywords: finite element; method solving; immersed finite; element method ... See more keywords
A modified immersed finite volume element method for elliptic interface problems
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DOI: 10.21914/anziamj.v62i0.14751
Abstract: This paper presents a new immersed finite volume element method for solving second-order elliptic problems with discontinuous diffusion coefficient on a Cartesian mesh. The new method possesses the local conservation property of classic finite volume… read more here.
Keywords: finite volume; method; volume element; volume ... See more keywords