QUADRATURE AND EXTRAPOLATION FOR THE VARIABLE COEFFICIENT ELLIPTIC EIGENVALUE PROBLEM

摘要

For the variable coefficient elliptic eigenvalue problem on a smooth domain or aconvex polygonal domain,a numerical quadrature scheme over triangles is used for computingthe coefficient of the resulting linear finite element system.The effect of numerical integrationis studied.The corresponding discrete eigenvalue with linear finite elements is shown to admitasymptotic error expansions for certain classes of“uniform”meshes.Hence,the Richardsonextrapolation increases the accuracy of the scheme from second to fourth order.