Convergence of Finite-difference Schemes for Poisson's Equation With Boundary Condition of the Third Kind
Branislav Popović (1995)
Matematički Vesnik
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Displaying similar documents to “On the Construction of Finite Difference Schemes Approximating Generalized Solutions”
Convergence of Finite-difference Schemes for Poisson's Equation With Boundary Condition of the Third Kind
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Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both...
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Divergence of FEM: Babuška-Aziz triangulations revisited
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By re-examining the arguments and counterexamples in I. Babuška, A. K. Aziz (1976) concerning the well-known maximum angle condition, we study the convergence behavior of the linear finite element method (FEM) on a family of distorted triangulations of the unit square originally introduced by H. Schwarz in 1880. For a Poisson problem with polynomial solution, we demonstrate arbitrarily slow convergence as well as failure of convergence if the distortion of the triangulations grows sufficiently...