Galerkin approximations for the linear parabolic equation with the third boundary condition

I. Faragó, Sergey Korotov, Pekka Neittaanmäki

Research output: Contribution to journalArticle

Abstract

We solve a linear parabolic equation in ℝ d, d ≥ 1, with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the θ-method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.

Original languageEnglish
Pages (from-to)111-128
Number of pages18
JournalApplications of Mathematics
Volume48
Issue number2
DOIs
Publication statusPublished - 2003

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Galerkin Approximation
Parabolic Equation
Linear equation
Discretization
Boundary conditions
Finite element method
Nonhomogeneous Boundary Conditions
Rate of Convergence
Finite Element Method
Projection
Approximation
Generalization

Keywords

  • elliptic projection
  • finite element method
  • fully discretized scheme
  • linear parabolic equation
  • semidiscretization
  • third boundary condition

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Galerkin approximations for the linear parabolic equation with the third boundary condition. / Faragó, I.; Korotov, Sergey; Neittaanmäki, Pekka.

In: Applications of Mathematics, Vol. 48, No. 2, 2003, p. 111-128.

Research output: Contribution to journalArticle

Faragó, I. ; Korotov, Sergey ; Neittaanmäki, Pekka. / Galerkin approximations for the linear parabolic equation with the third boundary condition. In: Applications of Mathematics. 2003 ; Vol. 48, No. 2. pp. 111-128.
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