scholarly journals Exponential Convergence of hp-DGFEM for Elliptic Problems in Polyhedral Domains

2013 ◽  
pp. 57-73 ◽  
Author(s):  
Dominik Schötzau ◽  
Christoph Schwab ◽  
Thomas Wihler ◽  
Marcel Wirz
Keyword(s):  
Exponential Convergence ◽  
Elliptic Problems

Exponential convergence in entropy and Wasserstein for McKean–Vlasov SDEs

2021 ◽  
Vol 206 ◽  
pp. 112259
Author(s):  
Panpan Ren ◽  
Feng-Yu Wang
Keyword(s):  
Exponential Convergence

scholarly journals Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Borsos ◽  
János Karátson
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Iterative Solvers ◽  
Finite Element Solution ◽  
Element Solution ◽  
Nonlinear Beam ◽  
Quasi Newton

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

Multiple solutions for nonlocal elliptic problems with concave–convex nonlinearities and weights

2021 ◽  
pp. 207-218
Author(s):  
Safia Benmansour ◽  
Atika Matallah ◽  
Mustapha Meghnafi
Keyword(s):  
Multiple Solutions ◽  
Elliptic Problems

scholarly journals A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

2021 ◽  
Vol 47 (3) ◽  
Author(s):  
Timon S. Gutleb
Keyword(s):  
Open Source ◽  
Spectral Method ◽  
Jacobi Polynomial ◽  
Numerical Experiments ◽  
Exponential Convergence ◽  
Analytic Solutions ◽  
Convolution Type ◽  
Volterra Equations ◽  
Polynomial Bases ◽  
Sparsity Structure

AbstractWe present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods.

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