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1D Painless Multi-level Automatic Goal-Oriented h and p Adaptive Strategies Using a Pseudo-Dual Operator
The main idea of our Goal-Oriented Adaptive (GOA) strategy is based on performing global and uniform h- or p-refinements (for h- and p-adaptivity, respectively) followed by a coarsening step, where some basis functions are ...
Explicit-in-Time Goal-Oriented Adaptivity
Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of ...
Quantities of interest for surface based resistivity geophysical measurements
The objective of traditional goal-oriented strategies is to construct an optimal mesh that minimizes the problem size needed to achieve a user prescribed tolerance error for a given quantity of interest (QoI). Typical ...
Goal-oriented adaptivity using unconventional error representations for the 1D Helmholtz equation
In this work, the error of a given output functional is represented using bilinear forms that are different from those given by the adjoint problem. These representations can be employed to design novel h, p, and hp ...
Simulation of marine controlled source electromagnetic measurements using a parallel fourier hp-finite element method
We introduce a new numerical method to simulate geophysical marine controlled source electromagnetic (CSEM) measurements for the case of 2D structures and finite 3D sources of electromagnetic (EM) excitation. The method ...