Reliable Methods for Computer Simulation: Error Control and a Posteriori Estimates
Reliable Methods for Computer Simulation: Error Control and a Posteriori Estimates
Computing with Hp-Adaptive Finite Elements, Vol. 2: Frontiers Three Dimensional Elliptic and Maxwell Problems with Applications
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The classical a posteriori error estimates are mostly oriented to the use in the finite element h-methods while the contemporary higher-order hp-methods usually require new approaches in a posteriori error estimation. These methods hold a very important position among adaptive numerical procedures for solving ordinary as well as partial differential equations arising from various technical applications. In the paper, we are concerned with a review and comparison of error estimation procedures for the biharmonic and some more general fourth order partial differential problems with special regards to the needs of the hp-method. We point out some advantages and drawbacks of analytical and computational a posteriori error estimates.