Session Time & Room : 4C (Aug.24, 13:20-15:00) @E506
Type : Proposal of Minisymposium
Abstract : In this mini-symposium we will focus on recent efforts in developing various numerical approaches for solving the oblique derivative boundary volume problems. Namely, we will apply the finite element, finite volume and boundary element methods to solve different engineering problems which involve the oblique derivatives.
[02007] The finite element method for solving the oblique derivative boundary value problems in geodesy
Author(s) :
Marek Macák (Slovak University of Technology )
Zuzana Minarechová (Slovak University of Technology )
Karol Mikula (Slovak University of Technology )
Robert Cunderlik (Slovak University of Technology )
Abstract : We present approach to approximate the solution of the Laplace equation with an oblique derivative boundary condition by the finite element method. For this approach we perform testing experiments to study its behaviour and convergence. Finally, the usefulness of this approach is demonstrated by using it to gravity field modelling, namely, to approximate the solution of a geodetic boundary value problem in Himalayas.
[02121] Curvature and Torsion of Gravitational Plumb Lines
Author(s) :
Zhi Yin (Jiangsu Ocean University)
Nico Sneeuw (University of Stuttgart)
Keifei Zhang (China University of Mining and Technology)
Abstract : In our previous research, we reformulate the gravitational field in terms of a potential flow; the gravitational vector field is mapped onto a potential-flow velocity field, in which the plumb line and the stream line are equivalent to each other. Here, we further investigate the curvature and the torsion of a gravitational plumb line by utilizing the fundamental equations of the potential flow. We expect them to have a good practical application in exploration geophysics.
[02131] The finite volume method for solving the oblique derivative BVP in geodesy
Author(s) :
Zuzana Minarechová (Slovak University of Technology)
Marek Macák (Slovak University of Technology )
Karol Mikula (Slovak University of Technology)
Róbert Čunderlík (Slovak University of Technology)
Abstract : We formulate the oblique derivative boundary value problem applied in gravity field and present two approaches to its solution by the finite volume method. In the first approach, the oblique derivative in the boundary condition is decomposed into normal and two tangential components and approximated by the central scheme. In the second approach, the oblique derivative in the boundary condition is treated by the first order upwind scheme. Both approaches are tested by various experiments.
[02887] Finite Volume Approximate Solutions of Some Oblique Derivative Boundary Value Problems and Applications
Author(s) :
Abdallah BRADJI (University of Annaba-Algeria)
Abstract : In this work, we review previous works on FVMs (Finite Volume methods) for Elliptic and Parabolic equations with oblique derivatives boundary conditions. We start by the first two works with Gallouet (Aix-Marseille University, France) which dealt with FV on the so-called Admissible meshes for Elliptic equations.
We subsequently describe our work with Fuhrmann (WIAS, Berlin-Germany) which dealt with FV using the nonconforming meshes and the SUSHI for Elliptic and Parabolic equations with oblique derivatives boundary conditions.
Finally, we focus on FVMs for Elliptic equations with mixed oblique boundary equations and application to Inverse Problems. This work is done jointly with Lesnic (Leeds University, UK).
We sketch at the end some works, related to the subject, which are in progress.
