부산대학교 도서관

The authors present an adaptive algorithm for one-dimensional ellipticboundary value problems solved with $hp$ finite elements. They provethat with the proposed scheme the error in the energy norm decreasesmonotonically at each step. Numerical experiments show that thedecrease follows an exponential law, though a formal proof ofoptimality is still lacking.\parThe method is based on a residual based a posteriori error estimatorand on the use of a carefully selected set of refinement patterns. Theadaptation procedure is formally extendable in higher dimension,though the cost of testing different refinement patterns could behigh. No coarsening step has been considered in this work. Yet, thetheoretical result leading to the monotone decrease of the errorcannot be directly extended to higher dimensions since $p$-uniformequivalence between the discretisation error and the proposedresidual-based estimation has been proved only in 1D.