Journal of Earth Science

, Volume 26, Issue 6, pp 821–826

# A goal-oriented adaptive finite element method for 3D resistivity modeling using dual-error weighting approach

• Yixin Ye
• Xiangyun Hu
• Dong Xu
Article

## Abstract

A goal-oriented adaptive finite element (FE) method for solving 3D direct current (DC) resistivity modeling problem is presented. The model domain is subdivided into unstructured tetrahedral elements that allow for efficient local mesh refinement and flexible description of complex models. The elements that affect the solution at each receiver location are adaptively refined according to a goal-oriented posteriori error estimator using dual-error weighting approach. The FE method with adapting mesh can easily handle such structures at almost any level of complexity. The method is demonstrated on two synthetic resistivity models with analytical solutions and available results from integral equation method, so the errors can be quantified. The applicability of the numerical method is illustrated on a resistivity model with a topographic ridge. Numerical examples show that this method is flexible and accurate for geometrically complex situations.

## Key Words

adaptive finite element dual-error weighting approach unstructured mesh 3D resistivity

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