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Advanced Numerical Methods in the Mathematical Sciences

Randolph Bank, University of California at San Diego
Some Recent Results for Adaptive Finite Elements


We will discuss our ongoing investigation of adaptive strategies for finite element equations. We show first that under modest assumptions, any robust and efficient a posteriori error indicator must behave as a simple interpolation error for the exact finite element solution. We then use the interpolation error to study several popular \(h\) and \(hp\) adaptive algorithms.