Abstract
A nonconforming mixed finite element method for nonlinear hyperbolic equations is discussed. Existence and uniqueness of the solution to the discrete problem are proved. Priori estimates of optimal order are derived for both the displacement and the stress.
Highlights
In this paper, we discuss a nonconforming mixed finite element method for the following nonlinear hyperbolic initial and boundary value problem.b u u utt X,t a g X u u,t, x, y f u, x, t T (1)In order to describe the results briefly, we suppose that Equation (1) satisfy following assumptions on the data: 1) a u and b u are smooth and there exist constants co, c1, a0 and a1 satisfyingIn the present work, we focus on the nonconforming mixed finite element approximation scheme for nonlinear hyperbolic equations
Priori estimates of optimal order are derived for both the displacement and the stress
We focus on the nonconforming mixed finite element approximation scheme for nonlinear hyperbolic equations
Summary
We discuss a nonconforming mixed finite element method for the following nonlinear hyperbolic initial and boundary value problem.b u u utt X,t a g X u u,t , x, y f u , x, t T (1)In order to describe the results briefly, we suppose that Equation (1) satisfy following assumptions on the data: 1) a u and b u are smooth and there exist constants co , c1, a0 and a1 satisfyingIn the present work, we focus on the nonconforming mixed finite element approximation scheme for nonlinear hyperbolic equations. A nonconforming mixed finite element method for nonlinear hyperbolic equations is discussed. Existence and uniqueness of the solution to the discrete problem are proved. Priori estimates of optimal order are derived for both the displacement and the stress.
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