论文信息 - Time-Space Discretization of the Nonlinear Hyperbolic System utt = div (\sigma(Du)+ Dut)

Time-Space Discretization of the Nonlinear Hyperbolic System utt = div (\sigma(Du)+ Dut)

The numerical treatment of the hyperbolic system of nonlinear wave equations with linear viscosity, utt = div(σ(Du) +Dut), is studied for a large class of globally Lipschitz continuous functions σ, including nonmonotone stress-strain relations. The analyzed method combines an implicit Euler scheme in time with Courant (continuous and piecewise affine) finite elements in space for a class of varying time steps with varying meshes. Explicit a priori error bounds in L∞(L2), L2(W 1,2), and W 1,2(L2) are established for the solutions of the fully discrete scheme.

Carsten Carstensen | Georg Dolzmann | C. Carstensen | G. Dolzmann

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