Journal ArticleDOI
Space–time adaptive splitting scheme for the numerical simulation of polycrystallization
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TLDR
In this paper, a space-time adaptive splitting scheme for polycrystallization processes described by a two-field phase field model is proposed, based on an implicit discretization in time which allows decoupling of the system in the sense that at each time step minimization problems in ϕ and Θ have to be solved successively.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2022-04-01. It has received 0 citations till now. The article focuses on the topics: Discretization & Discretization.read more
References
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Optimization and nonsmooth analysis
TL;DR: The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.
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Convex analysis and variational problems
Ivar Ekeland,Roger Téman +1 more
TL;DR: In this article, the authors consider non-convex variational problems with a priori estimate in convex programming and show that they can be solved by the minimax theorem.
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Functions of Bounded Variation and Free Discontinuity Problems
TL;DR: The Mumford-Shah functional minimiser of free continuity problems as mentioned in this paper is a special function of the Mumfordshah functional and has been shown to be a function of free discontinuity set.
Journal ArticleDOI
A convergent adaptive algorithm for Poisson's equation
TL;DR: In this paper, a converging adaptive algorithm for linear elements applied to Poisson's equation in two space dimensions is presented, and it is proved that the error, measured in the energy norm, decreases at a constant rate in each step until a prescribed error bound is reached.
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