hp finite elements
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scholarly journals hp-FEM for the fractional heat equation

2020 ◽  
Author(s):  
Jens Markus Melenk ◽  
Alexander Rieder
Keyword(s):  
Finite Elements ◽  
Heat Equation ◽  
Exponential Convergence ◽  
Time Dependent ◽  
Nonlocal Operator ◽  
Time Stepping ◽  
Fractional Heat Equation ◽  
Time Dependent Problem ◽  
Hp Finite Elements ◽  
Abstract Framework

Abstract We consider a time-dependent problem generated by a nonlocal operator in space. Applying for the spatial discretization a scheme based on $hp$-finite elements and a Caffarelli–Silvestre extension we obtain a semidiscrete semigroup. The discretization in time is carried out by using $hp$-discontinuous Galerkin based time stepping. We prove exponential convergence for such a method in an abstract framework for the discretization in the spatial domain $\varOmega $.

scholarly journals $hp$-Finite Elements for Fractional Diffusion

2018 ◽  
Vol 56 (4) ◽  
pp. 2345-2374 ◽  
Author(s):  
Dominik Meidner ◽  
Johannes Pfefferer ◽  
Klemens Schürholz ◽  
Boris Vexler
Keyword(s):  
Finite Elements ◽  
Fractional Diffusion ◽  
Hp Finite Elements

scholarly journals Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures

2015 ◽  
Author(s):  
Sven Burger ◽  
Philipp Gutsche ◽  
Martin Hammerschmidt ◽  
Sven Herrmann ◽  
Jan Pomplun ◽  
...  
Keyword(s):  
Finite Elements ◽  
Electromagnetic Fields ◽  
Optical Devices ◽  
Hp Finite Elements

scholarly journals Modeling of bone conduction of sound in the human head using hp-finite elements: Code design and verification

2011 ◽  
Vol 200 (21-22) ◽  
pp. 1757-1773 ◽  
Author(s):  
L. Demkowicz ◽  
P. Gatto ◽  
J. Kurtz ◽  
M. Paszyński ◽  
W. Rachowicz ◽  
...  
Keyword(s):  
Finite Elements ◽  
Bone Conduction ◽  
Human Head ◽  
Code Design ◽  
Hp Finite Elements
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