A priori error estimates for finite element methods for H(2;1)-elliptic equations - Archive ouverte HAL Access content directly
Journal Articles Numerical Functional Analysis and Optimization Year : 2014

A priori error estimates for finite element methods for H(2;1)-elliptic equations

, , (1) ,
1
Thomas Apel
  • Function : Author
T. Flaig
  • Function : Author
Thomas G Flaig
  • Function : Author

Abstract

The convergence of finite element methods for linear elliptic boundary value problems of second and forth order is well understood. In this article, we introduce finite element approximations of some linear semi-elliptic boundary value problem of mixed order on a two-dimensional rectangular domain Q. The equation is of second order in one direction and forth order in the other and appears in the optimal control of parabolic partial differential equations if one eliminates the control and the state (or the adjoint state) in the first order optimality conditions. We establish a regularity result and estimate for the finite element error of conforming approximations of this equation. The finite elements in use have a tensor product structure, in one dimension we use linear, quadratic or cubic Lagrange elements in the other dimension cubic Hermite elements. For these elements, we prove the error bound O(h 2 + τk) in the energy norm and O((h 2 + τk)(h 2 + τ)) in the L 2(Q)-norm.
Not file

Dates and versions

hal-03138800 , version 1 (11-02-2021)

Identifiers

Cite

Thomas Apel, T. Flaig, Serge Nicaise, Thomas G Flaig. A priori error estimates for finite element methods for H(2;1)-elliptic equations. Numerical Functional Analysis and Optimization, 2014, 35 (2), pp.153-176. ⟨10.1080/01630563.2013.811600⟩. ⟨hal-03138800⟩
6 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More