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In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assumed to be quasiuniform. In the present paper we show a resolvent estimate, in one and two space dimensions,...
In recent years several papers have been devoted to stability
and smoothing properties in maximum-norm of
finite element discretizations of parabolic problems.
Using the theory of analytic semigroups it has been possible
to rephrase such properties as bounds for the resolvent
of the associated discrete elliptic operator. In all these
cases the triangulations of the spatial domain has been
assumed to be quasiuniform. In the present paper we
show a resolvent estimate, in one and two space dimensions,
under...
We consider the initial value problem for an infinite system of differential-functional equations of parabolic type. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. The solutions are obtained by the monotone iterative method. We prove theorems on weak partial differential-functional inequalities as well the existence and uniqueness theorems in the class of continuous bounded functions and in the class of functions satisfying...
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