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This paper is concerned with the proof of existence and numericalapproximation of large-data global-in-time Young measure solutions toinitial-boundary-value problems for multidimensional nonlinear parabolicsystems of forward-backward type of the form $\partial_t u - \mbox{div}(a(Du))+ Bu = F$, where $B \in \mathbb{R}^{m \times m}$, $Bv \cdot v \geq 0$ for all$v \in \mathbb{R}^m$, $F$ is an $m$-component vector-function defined on abounded open Lipschitz domain $\Omega \subset \mathbb{R}^n$, and $a$ is alocally Lipschitz mapping of the form $a(A)=K(A)A$, where $K\,:\, \mathbb{R}^{m\times n} \rightarrow \mathbb{R}$. The function $a$ may have a nonstandardgrowth rate, in the sense that it is permitted to have unequal lower and uppergrowth rates. Furthermore, $a$ is not assumed to be monotone, nor is it assumedto be the gradient of a potential. Problems of this type arise in mathematicalmodels of the atmospheric boundary layer and fall beyond the scope of monotoneoperator theory. We develop a numerical algorithm for the approximate solutionof problems in this class, and we prove the convergence of the algorithm to aYoung measure solution of the system under consideration.

Numerical Approximation of Young Measure Solutions to Parabolic Systems of Forward-Backward Type