scholarly journals Numerical Experiments Using MATLAB: Superconvergence of Conforming Finite, Element Approximation for Second Order, Elliptic Problems

2018 ◽  
Vol 09 (06) ◽  
pp. 691-701
Author(s):  
Anna Harris ◽  
Stephen Harris ◽  
Camille Gardner ◽  
Tyrone Brock
Keyword(s):  
Finite Element ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Finite Element Approximation ◽  
Second Order ◽  
Element Approximation ◽  
Conforming Finite Element ◽  
Second Order Elliptic Problems

scholarly journals Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow

2020 ◽  
Vol 30 (05) ◽  
pp. 847-865
Author(s):  
Gabriel Barrenechea ◽  
Erik Burman ◽  
Johnny Guzmán
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Inviscid Flow ◽  
Element Approximation ◽  
Well Posedness ◽  
Hodge Laplacian ◽  
Conforming Finite Element ◽  
Velocity Approximation

We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using [Formula: see text](div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the [Formula: see text]-norm of order [Formula: see text]. We also prove error estimates for the pressure error in the [Formula: see text]-norm.

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