In this paper, we discuss an -discontinuous Galerkin finite
element method (-DGFEM) for the laser surface hardening of
steel, which is a constrained optimal control problem governed by a
system of differential equations, consisting of an ordinary
differential equation for austenite formation and a semi-linear
parabolic differential equation for temperature evolution. The space
discretization of the state variable is done using an -DGFEM,
time and control discretizations are based on a discontinuous
Galerkin...
In this paper, we discuss an -discontinuous Galerkin finite
element method (-DGFEM) for the laser surface hardening of
steel, which is a constrained optimal control problem governed by a
system of differential equations, consisting of an ordinary
differential equation for austenite formation and a semi-linear
parabolic differential equation for temperature evolution. The space
discretization of the state variable is done using an -DGFEM,
time and control discretizations are based on a discontinuous
Galerkin...
Estimates for the combined effect of boundary approximation and numerical integration on the approximation of (simple) eigenvalues and eigenvectors of 4th order eigenvalue problems with variable/constant coefficients in convex domains with curved boundary by an isoparametric mixed finite element method, which, in the particular case of bending problems of aniso-/ortho-/isotropic plates with variable/constant thickness, gives a simultaneous approximation to bending moment tensor field and displacement...
Error estimates for the mixed finite element solution of
4th order elliptic problems with variable coefficients, which,
in the particular case of aniso-/ortho-/isotropic plate bending problems,
gives a direct, simultaneous approximation to bending moment tensor
field and displacement field
, have been developed considering the combined effect of
boundary approximation and numerical integration.
Estimates for the combined effect of boundary
approximation and numerical integration on the approximation of
(simple) eigenvalues and eigenvectors of 4th order
eigenvalue problems with variable/constant coefficients
in convex domains with curved boundary by an isoparametric mixed
finite element method, which,
in the particular case of bending problems of
aniso-/ortho-/isotropic plates with variable/constant
thickness, gives a simultaneous approximation to bending moment
tensor field and
displacement...
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