Mixed finite element methods are developed to approximate the solution of the Dirichlet problem for the most general quasi-linear second-order elliptic operator in divergence form. Existence and uniqueness of the approximation are proved, and optimal error estimates in L2 are demonstrated for both the scalar and vector functions approximated by the method. Error estimates Newton’s method is presented and analyzed to solve the are nonlinear also derived algebraic in equations. Lq, 2_q_+c.
Bibliographical noteFunding Information:
Received by the editors April 20, 1993; accepted for publication (in revised form) December 10, 1993. This work was supported in part by the Purdue Research Foundation. Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395. Current address: Dipartimento di Matematica, Universit di Trento, 38050 Povo, Italy (park(C)volterra. science,un+/-tn, it).
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics