Recovery Type A Posteriori Error Estimates

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Zhang The investigator studies a posteriori error estimates forthe numerical solution of partial differential equations. Hedevelops general mathematical theory for recovery type aposteriori error estimates and explores a new gradient recoverytechnique and associated error estimator that has betterproperties than the existing ones. Some recent mathematicaltheory in finite element superconvergence, asymptotic regularity,as well as improved interior analysis, is employed in theproject. Numerical solutions of differential equations are essentialin all areas of science and engineering. But the numericalsolutions are often less accurate than one desires. It istherefore important to estimate the error and to use thatestimate to improve the accuracy. Error estimation is essentialfor effective and reliable computation. Recovery type aposteriori error estimates are post-processing techniques thatuse a numerical solution produced by some base method to produceapproximations that are of higher order of accuracy than the basemethod solution, and that combine the two solutions to estimatethe error in the approximate solution. The techniques are commonbut not theoretically understood or justified, especially fornonuniform meshes. The investigator studies these methods anddevelops a new kind of recovery type error estimator that offerssome advantages over present alternatives. The project fills agap between engineering practice and mathematical theoreticaldevelopment. The project includes training of graduate students.There are interdisciplinary connections with engineers and otherscientific computing disciplines, and with industry.