## Some new $$L^{\infty}$$-error estimates for mixed finite element methods.(English)Zbl 0624.65098

L$${}^{\infty}$$-error estimates of nearly optimal order and regularity are derived through the use of weighted $$L^ 2$$-norms for the solution of linear second order elliptic and parabolic problems using low-indexed mixed finite elements of Raviart-Thomas-Nedelec type.

### MSC:

 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 35K20 Initial-boundary value problems for second-order parabolic equations

### Keywords:

error estimates; mixed finite elements