Numerical approximation of planar oblique derivative problems in nondivergence form

D. Gallistl

doi:10.1090/mcom/3371

Numerical approximation of planar oblique derivative problems in nondivergence form

D. Gallistl (Corresponding Author)

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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 language	English
Pages (from-to)	1091-1119
Number of pages	29
Journal	Mathematics of computation
Volume	88
Issue number	317
DOIs	https://doi.org/10.1090/mcom/3371
Publication status	Published - May 2019

Keywords

Cordes coefficents
Oblique derivative problem
A posteriori error analysis
A priori error analysis
Nondivergence form
n/a OA procedure

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10.1090/mcom/3371

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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.",

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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.

KW - Cordes coefficents

KW - Oblique derivative problem

KW - A posteriori error analysis

KW - A priori error analysis

KW - Nondivergence form

KW - n/a OA procedure

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U2 - 10.1090/mcom/3371

DO - 10.1090/mcom/3371

M3 - Article

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VL - 88

SP - 1091

EP - 1119

JO - Mathematics of computation

JF - Mathematics of computation

IS - 317

ER -

Numerical approximation of planar oblique derivative problems in nondivergence form

Abstract

Keywords

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