A compactness criterion in the space of Hilbert-Schmidt operators

1975 ◽  
Vol 26 (4) ◽  
pp. 433-435
Author(s):  
G. P. Butsan
Keyword(s):  
Compactness Criterion

scholarly journals S-adic version of Minkowski's geometry of numbers and Mahler's compactness criterion

2017 ◽  
Vol 174 ◽  
pp. 150-163 ◽  
Author(s):  
Dmitry Kleinbock ◽  
Ronggang Shi ◽  
George Tomanov
Keyword(s):  
Geometry Of Numbers ◽  
Compactness Criterion

scholarly journals A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology

2019 ◽  
Vol 40 (2) ◽  
pp. 1544-1576 ◽  
Author(s):  
Verónica Anaya ◽  
Mostafa Bendahmane ◽  
David Mora ◽  
Mauricio Sepúlveda
Keyword(s):  
Cardiac Electrophysiology ◽  
A Priori Estimates ◽  
A Priori ◽  
Reaction Diffusion ◽  
Optimal Order ◽  
Computational Domain ◽  
Virtual Element Method ◽  
Compactness Criterion ◽  
Virtual Element ◽  
Element Method

AbstractWe present a virtual element method (VEM) for a nonlocal reaction–diffusion system of the cardiac electric field. For this system, we analyze an $H^1$-conforming discretization by means of VEM that can make use of general polygonal meshes. Under standard assumptions on the computational domain, we establish the convergence of the discrete solution by considering a series of a priori estimates and by using a general $L^p$ compactness criterion. Moreover, we obtain optimal order space-time error estimates in the $L^2$ norm. Finally, we report some numerical tests supporting the theoretical results.

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