scholarly journals A Priori Error Estimates for the Finite Element Discretization of Elliptic Parameter Identification Problems with Pointwise Measurements

2005 ◽  
Vol 44 (5) ◽  
pp. 1844-1863 ◽  
Author(s):  
R. Rannacher ◽  
B. Vexler
Keyword(s):  
Finite Element ◽  
Parameter Identification ◽  
Error Estimates ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Identification Problems ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Parameter Identification Problems ◽  
Priori Error Estimates

scholarly journals A priori error estimates for the space-time finite element approximation of a quasilinear gradient enhanced damage model

2021 ◽  
Author(s):  
Marita Holtmannspötter
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
A Priori ◽  
Damage Model ◽  
Space Time ◽  
A Priori Error Estimates ◽  
Element Approximation ◽  
Element Discretization ◽  
Priori Error Estimates ◽  
Almost All

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a quasilinear gradient enhanced damage model. The model equations are of a special structure as the state equation consists of two quasilinear elliptic PDEs which have to be fulfilled at almost all times coupled with a nonsmooth, semilinear ODE that has to hold true in almost all points in space. The system is discretized by a constant discontinuous Galerkin method in time and usual conforming linear finite elements in space. Numerical experiments are added to illustrate the proven rates of convergence.

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