Approximation of partial differential equations on compact resistance spaces

Abstract We consider linear partial differential equations on resistance spaces that are uniformly elliptic and parabolic in the sense of quadratic forms involve abstract gradient divergence terms. Our main interest is to provide graph metric approximations for their unique solutions. For families with different coefficients a single compact space we prove solutions have accumulation points respect uniform convergence space, provided remain bounded. If sequence converge suitably, along subsequence. special case local finitely ramified sets also sequences approximating set from within. Under suitable assumptions (extensions of) linearizations accumulate or even subsequence solution target equation set. The results cover discrete approximations, both discussed.