Local H1-norm error analysis of a mixed finite element method for a time-fractional biharmonic equation

2022 ◽  
Vol 173 ◽  
pp. 211-221
Author(s):  
Chaobao Huang ◽  
Na An ◽  
Hu Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Analysis ◽  
Biharmonic Equation ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Norm Error ◽  
Element Method

scholarly journals MIXED FINITE ELEMENT FORMULATION OF THE BIHARMONIC EQUATION

2005 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
A. D. GARNADI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimate ◽  
Biharmonic Equation ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Element Formulation ◽  
Abstract Setting ◽  
First Time ◽  
Element Method

<p>We will provide an abstract setting for mixed finite element method for biharmonic equation. The abstract setting casts mixed finite element method for first biharmonic equation and sec- ond biharmonic equation into a single framework altogether. We provide error estimates for both type biharmonic equation, and for the first time an error estimate for the second biharmonic equation.</p>

scholarly journals The Time DiscontinuousH1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Hong Yu ◽  
Tongjun Sun ◽  
Na Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Approximate Solutions ◽  
Piecewise Polynomial ◽  
Sobolev Equations ◽  
Time Variables ◽  
Norm Error ◽  
Element Method

We combine theH1-Galerkin mixed finite element method with the time discontinuous Galerkin method to approximate linear Sobolev equations. The advantages of these two methods are fully utilized. The approximate schemes are established to get the approximate solutions by a piecewise polynomial of degree at mostq-1with the time variable. The existence and uniqueness of the solutions are proved, and the optimalH1-norm error estimates are derived. We get high accuracy for both the space and time variables.

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