POINTWISE ERROR ESTIMATES FOR MIXED FINITE-ELEMENT METHODS FOR QUASILINEAR SECOND ORDER ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
Abstract
This thesis deals with the approximation of the solution of second order quasi-linear elliptic equations in two dimensions by mixed finite element methods. Raviart-Thomas-Nedelec elements are used for the approximation. In the case of the mildest nonlinearity as well as in the general linear case, an upper bound for the pointwise error is established which is optimal both in rate and in regularity required of the solution of the differential problem. A similar optimal result is obtained for the vector variable approximated with the mixed method.
Degree
Ph.D.
Subject Area
Mathematics
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