This paper considers semi-discrete and fully discrete mixed finite element discretizations for Maxwell-model-based problems of wave propagation in 2-dimensional linear viscoelastic solid. A large class of existing mixed conforming finite elements for elasticity are used in the spatial discretization. In the fully discrete scheme, a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of displacement and stress . Error estimates of the two schemes, as well as an unconditional stability result for the fully discrete scheme, are derived. Numerical experiments are provided which apply two low order rectangular elements in the spatial discretization .
Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid. This mixed finite element framework allows the use of a large class of existing mixed conforming finite elements for elasticity in the spatial discretization. In the fully discrete scheme, a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of stress and velocity variables . Error estimates of the semi-discrete and fully discrete schemes, as well as an unconditional stability result for the fully discrete scheme, are derived. Numerical experiments are provided to verify the theoretical results .
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This paper considers semi-discrete
Semi-discrete
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discretizations
methods are considered
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2-dimensional
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A
This mixed finite element framework allows the use of a
D
are used
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displacement and stress
stress and velocity variables
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two
semi-discrete and fully discrete
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which apply two low order rectangular elements in the spatial discretization
to verify the theoretical results