Numerical approximation of planar oblique derivative problems in nondivergence form

D. Gallistl (Corresponding Author)

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

A numerical method for approximating a uniformly elliptic oblique derivative problem in two-dimensional simply-connected domains is proposed. The numerical scheme employs a mixed formulation with piecewise affine functions on curved finite element domains. The direct approximation of the gradient of the solution turns the oblique derivative boundary condition into an oblique direction condition. A priori and a posteriori error estimates as well as numerical computations on uniform and adaptive meshes are provided.
Original languageEnglish
Pages (from-to)1091-1119
Number of pages29
JournalMathematics of computation
Volume88
Issue number317
DOIs
Publication statusPublished - May 2019

Fingerprint

Oblique
Numerical Approximation
Derivatives
Derivative
Numerical methods
Affine Function
Adaptive Mesh
Mixed Formulation
A Posteriori Error Estimates
Boundary conditions
Numerical Computation
Numerical Scheme
Numerical Methods
Finite Element
Gradient
Approximation
Form

Keywords

  • Cordes coefficents
  • Oblique derivative problem
  • a posteriori error analysis
  • a priori error analysis
  • nondivergence form

Cite this

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Numerical approximation of planar oblique derivative problems in nondivergence form. / Gallistl, D. (Corresponding Author).

In: Mathematics of computation, Vol. 88, No. 317, 05.2019, p. 1091-1119.

Research output: Contribution to journalArticleAcademicpeer-review

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N2 - A numerical method for approximating a uniformly elliptic oblique derivative problem in two-dimensional simply-connected domains is proposed. The numerical scheme employs a mixed formulation with piecewise affine functions on curved finite element domains. The direct approximation of the gradient of the solution turns the oblique derivative boundary condition into an oblique direction condition. A priori and a posteriori error estimates as well as numerical computations on uniform and adaptive meshes are provided.

AB - A numerical method for approximating a uniformly elliptic oblique derivative problem in two-dimensional simply-connected domains is proposed. The numerical scheme employs a mixed formulation with piecewise affine functions on curved finite element domains. The direct approximation of the gradient of the solution turns the oblique derivative boundary condition into an oblique direction condition. A priori and a posteriori error estimates as well as numerical computations on uniform and adaptive meshes are provided.

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KW - Oblique derivative problem

KW - a posteriori error analysis

KW - a priori error analysis

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