Simulations of 3D DC borehole resistivity measurements with a goal-oriented \(hp\) finite-element method. Part II: Through-casing resistivity instruments

DOI10.1007/s10596-007-9061-yzbMath1148.78303OpenAlexW2129902260MaRDI QIDQ926005

David Pardo, Maciej Paszynski, Carlos Torres-Verdín

Publication date: 26 May 2008

Published in: Computational Geosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10596-007-9061-y

zbMATH Keywords

electrostaticsexponential convergencegoal-oriented adaptivity\(hp\) finite elementstrough-casing resistivity instruments

Mathematics Subject Classification ID

Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Electro- and magnetostatics (78A30)

Related Items (8)

Semi-analytical solutions for the problem of the electric potential set in a borehole with a highly conductive casing ⋮ A quadrature-free method for simulation and inversion of 1.5D direct current (DC) borehole measurements ⋮ Asymptotic models for the electric potential across a highly conductive casing ⋮ Using a graph grammar system in the finite element method ⋮ A hybrid method for inversion of 3D DC resistivity logging measurements ⋮ Fourier series expansion in a non-orthogonal system of coordinates for the simulation of 3D-DC borehole resistivity measurements ⋮ Fourier series expansion in a non-orthogonal system of coordinates for the simulation of 3D alternating current borehole resistivity measurements ⋮ Adjoint-based formulation for computing derivatives with respect to bed boundary positions in resistivity geophysics

Cites Work

• Verification of goal-oriented hp-adaptivity
• A fully automatic \(hp\)-adaptivity for elliptic PDEs in three dimensions
• \(H^1\), \(H\)(curl) and \(H\)(div)-conforming projection-based interpolation in three dimensions: Quasi-optimal \(p\)-interpolation estimates
• On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors
• Integration of \(hp\)-adaptivity and a two-grid solver for elliptic problems
• Two‐Dimensional High‐Accuracy Simulation of Resistivity Log ging‐While‐Drilling (LWD) Measurements Using a Self‐Adaptiv e Goal‐Oriented $hp$ Finite Element Method
• A goal-orientedhp-adaptive finite element method with electromagnetic applications. Part I: electrostatics
• Gaussian Spectral Rules for the Three-Point Second Differences: I. A Two-Point Positive Definite Problem in a Semi-Infinite Domain
• Gaussian spectral rules for second order finite-difference schemes

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