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In this paper, a high-accuracy H1-Galerkin mixed finite element method (MFEM) for strongly damped wave equation is studied by linear triangular finite element. By constructing a suitable extrapolation scheme, the convergence rates can be improved from 𝒪(h) to 𝒪(h3) both for the original variable u in H1(Ω) norm and for the actual stress variable p = ∇ut in H(div;Ω) norm, respectively. Finally, numerical results are presented to confirm the validity of the theoretical analysis and excellent performance of the proposed method.

The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc, using Fourier and generalized Laguerre functions. As an example, we consider a nonlinear strongly damped wave equation. The mixed spectral and pseudospectral schemes are proposed. The convergence is proved. Numerical results demonstrate the efficiency of this approach.

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Asymptotic Expansions and Extrapolations of H1-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation

Mixed Spectral and Pseudospectral Methods for a Nonlinear Strongly Damped Wave Equation in an Exterior Domain

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Asymptotic Expansions and Extrapolations of H1-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation

Mixed Spectral and Pseudospectral Methods for a Nonlinear Strongly Damped Wave Equation in an Exterior Domain