Strong Lp Convergence Associated with Rellich-type Discrete Compactness for Discontinuous Galerkin FEM
نویسندگان
چکیده
In a preceding paper, we proved the discrete compactness properties of Rellich type for some 2D discontinuous Galerkin finite element methods (DGFEM), that is, the strong L2 convergence of some subfamily of finite element functions bounded in an H1-like mesh-dependent norm. In this note, we will show the strong Lp convergence of the above subfamily for 1 ≤ p < ∞. To this end, we will utilize the duality mappings and special auxiliary problems. The results are applicable to numerical analysis of various semi-linear problems.
منابع مشابه
] 2011 - 04 Rellich - type Discrete Compactness for Some Discontinuous Galerkin FEM ∗
We deduce discrete compactness of Rellich type for some discontinuous Galerkin finite element methods (DGFEM) including hybrid ones, under fairly general settings on the triangulations and the finite element spaces. We make use of regularity of the solutions to an auxiliary second-order elliptic boundary value problem as well as the error estimates of the associated finite element solutions. Th...
متن کاملDiscrete compactness for a discontinuous Galerkin approximation of Maxwell's system
In this paper we prove the discrete compactness property for a discontinuous Galerkin approximation of Maxwell’s system on quite general tetrahedral meshes. As a consequence, a discrete Friedrichs inequality is obtained and the convergence of the discrete eigenvalues to the continuous ones is deduced using the theory of collectively compact operators. Some numerical experiments confirm the theo...
متن کاملConvergence of Discontinuous Time-stepping Schemes for a Robin Boundary Control Problem under Minimal Regularity Assumptions
The minimization of the energy functional having states constrained to semi-linear parabolic PDEs is considered. The controls act on the boundary and are of Robin type. The discrete schemes under consideration are discontinuous in time but conforming in space. Stability estimates are presented at the energy norm and at arbitrary times for the state, and adjoint variables. The estimates are deri...
متن کاملConvergence of Discontinuous Galerkin Approximations of an Optimal Control Problem Associated to Semilinear Parabolic Pde’s
A discontinuous Galerkin finite element method for an optimal control problem related to semilinear parabolic PDE’s is examined. The schemes under consideration are discontinuous in time but conforming in space. Convergence of discrete schemes of arbitrary order is proven. In addition, the convergence of discontinuous Galerkin approximations of the associated optimality system to the solutions ...
متن کاملLocal Discontinuous Galerkin Method for Diffusion Equations with Reduced Stabilization
We extend the results on minimal stabilization of Burman and Stamm (”Minimal stabilization of discontinuous Galerkin finite element methods for hyperbolic problems”, J. Sci. Comp., DOI: 10.1007/s10915-007-9149-5) to the case of the local discontinuous Galerkin methods on mixed form. The penalization term on the faces is relaxed to act only on a part of the polynomial spectrum. Stability in the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017