# Numerical approximation of planar oblique derivative problems in nondivergence form

D. Gallistl (Corresponding Author)

2 Citations (Scopus)

### 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 1091-1119 29 Mathematics of computation 88 317 https://doi.org/10.1090/mcom/3371 Published - May 2019

### Fingerprint

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

### Keywords

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

### Cite this

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title = "Numerical approximation of planar oblique derivative problems in nondivergence form",
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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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.

TY - JOUR

T1 - Numerical approximation of planar oblique derivative problems in nondivergence form

AU - Gallistl, D.

PY - 2019/5

Y1 - 2019/5

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.

KW - Cordes coefficents

KW - Oblique derivative problem

KW - a posteriori error analysis

KW - a priori error analysis

KW - nondivergence form

UR - http://www.scopus.com/inward/record.url?scp=85064505255&partnerID=8YFLogxK

U2 - 10.1090/mcom/3371

DO - 10.1090/mcom/3371

M3 - Article

VL - 88

SP - 1091

EP - 1119

JO - Mathematics of computation

JF - Mathematics of computation

SN - 0025-5718

IS - 317

ER -