Primal Hybrid Method For Quasilinear Parabolic Problems

In this article, a second order quasi-linear parabolic initial-boundary value problem is approximated by using primal hybrid finite element method and Lagrange multipliers. Semidiscrete and backward Euler based fully discrete schemes are discussed and optimal order error estimates are established by applying modified elliptic projection. Optimal order error estimates in maximum norm are also derived. Earlier results on maximum-norm superconvergence of the gradient in piecewise linear finite-element approximations of elliptic and parabolic problems are now carried over to quasilinear case using primal hybrid method. Finally, the results on numerical experiments confirm our theoretical findings.