Semi-discrete and fully discrete weak Galerkin finite element methods for a quasistatic Maxwell viscoelastic model
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This paper considers weak Galerkin finite element approximations for a quasistatic Maxwell viscoelastic model. The spatial discretization uses piecewise polynomials of degree k (k≥ 1) for the stress approximation, degree k+1 for the velocity approximation, and degree k for the numerical trace of velocity on the inter-element boundaries. The temporal discretization in the fully discrete method adopts a backward Euler difference scheme. We show the existence and uniqueness of the semi-discrete and fully discrete solutions, and derive optimal a priori error estimates. Numerical examples are provided to support the theoretical analysis.
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