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Thesis

A priori regularity results for discrete solutions to elliptic problems

Abstract:

This thesis is concerned with the development and analysis of a discrete counterpart of the well-known De-Giorgi-type regularity theory for solutions of elliptic partial differential equations in the setting of finite element approximations. We consider a finite element space consisting of piecewise affine functions on shape-regular triangulations of polyhedral Lipschitz domains Ω ⊂ R n . We identify conditions for the mesh and the data to prove a global a priori Hölder-norm bound for fini...

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Division:
MPLS
Department:
Mathematical Institute
Role:
Author

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Role:
Supervisor
Engineering and Physical Sciences Research Council More from this funder
The Clarendon Fund More from this funder
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
Language:
English
Deposit date:
2021-05-30

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