Mixed finite elements for second order elliptic problems in three variables
Numerische Mathematik
A priori estimates for mixed finite element methods for the wave equation
Computer Methods in Applied Mechanics and Engineering
Mixed finite element methods for elliptic problems
Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
SIAM Journal on Numerical Analysis
Discrete-Time Orthogonal Spline Collocation Methods for Vibration Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Nonlinear Analysis: Theory, Methods & Applications
An exact solution for variable coefficients fourth-order wave equation using the Adomian method
Mathematical and Computer Modelling: An International Journal
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
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Mixed finite element methods, explicit and implicit in time, for a fourth-order wave equation are considered in this paper. The optimal error estimates in the L^2 norm for velocity and moment and in the H^1 norm and L^2 norm for displacement are derived. These error estimates are proved by using a special interpolation operator on quasi-uniform rectangular meshes. The stabilities of the two schemes are also analyzed. In addition, three other kinds of mixed scheme are constructed. Numerical examples are provided to verify the theoretical results.