Index reduction for operator differential‐algebraic equations in elastodynamics

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AbstractIn space semi‐discretized equations of elastodynamics with weakly enforced Dirichlet boundary conditions lead to differential algebraic equations (DAE) of index 3. We rewrite the continuous model as operator DAE and present an index reduction technique on operator level. This means that a semi‐discretization leads directly to an index‐1 system. We present existence results for the operator DAE with nonlinear damping term and show that the reformulated operator DAE is equivalent to the original equations of elastodynamics. Furthermore, we show that index reduction and semi‐discretization in space commute if the discretization schemes are chosen in an appropriate way.