Now showing items 1-10 of 19
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 ...
Fast 2.5D Finite Element Simulations of Borehole Resistivity Measurements
We develop a rapid 2.5-dimensional (2.5D) finite element method for simulation of borehole resistivity measurements in transversely isotropic (TI) media. The method combines arbitrary high-order $H^1$ - and $H$ (curl)-conforming ...
A multi-domain decomposition-based Fourier finite element method for the simulation of 3D marine CSEM measurements
We introduce a multi-domain decomposition Fourier finite element (MDDFFE) method for the simulation of three-dimensional (3D) marine controlled source electromagnetic measurement (CSEM). The method combines a 2D finite ...
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 ...
Direct solvers performance on h-adapted grids
We analyse the performance of direct solvers when applied to a system of linear equations arising from an $h$-adapted, $C^0$ finite element space. Theoretical estimates are derived for typical $h$-refinement patterns arising ...
Some discrete maximum principles arising for nonlinear elliptic finite element problems
The discrete maximum principle (DMP) is an important measure of the qualitative reliability of the applied numerical scheme for elliptic problems. This paper starts with formulating simple sufficient conditions for the ...
On the maximum angle condition for the conforming longest-edge n-section algorithm for large values of n
In this note we introduce the conforming longest-edge $n$-section algorithm and show that for $n \ge 4$ it produces a family of triangulations which does not satisfy the maximum angle condition.
Unified modeling language description of the object-oriented multi-scale adaptive finite element method for step-and-flash imprint lithography simulations
In the first part of the paper we present the multi-scale simulation of the Step-and-Flash Imprint Lithography (SFIL), a modern patterning process. The simulation utilizes the hp adaptive Finite Element Method (hp-FEM) ...
Low cost a posteriori error estimators for an augmented mixed FEM in linear elasticity. Dedicated to Professor Rodolfo Rodríguez on the occasion of his 60th birthday.
We consider an augmented mixed finite element method applied to the linear elasticity problem and derive a posteriori error estimators that are simpler and easier to implement than the ones available in the literature. In ...