Discontinuous Galerkin method of lines for solving nonstationary singularly perturbed linear problems
نویسندگان
چکیده
منابع مشابه
A New Method for Solving Singularly Perturbed Boundary Value Problems
In this paper, a new initial value method for solving a class of nonlinear singularly perturbed boundary value problems with a boundary layer at one end is proposed. The method is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems (easy to use, modest problem preparation and ready computer implementation). Using singular perturbation anal...
متن کاملLocal Analysis of Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem
In this paper we will present the local stability analysis and local error estimate for the local discontinuous Galerkin (LDG)method, when solving the time-dependent singularly perturbed problems in one dimensional spacewith a stationary outflow boundary layer. Based on a general framework on the local stability, we obtain the optimal error estimate out of the local subdomain, which is nearby t...
متن کاملUniform superconvergence analysis of the discontinuous Galerkin method for a singularly perturbed problem in 1-D
It has been observed from the authors’ numerical experiments (2007) that the Local Discontinuous Galerkin (LDG) method converges uniformly under the Shishkin mesh for singularly perturbed two-point boundary problems of the convection-diffusion type. Especially when using a piecewise polynomial space of degree k, the LDG solution achieves the optimal convergence rate k+1 under the L2-norm, and a...
متن کاملA Discontinuous Galerkin Method for Solving Total Variation Minimization Problems
The minimization of functionals which are formed by an L2-term and a Total Variation (TV) term play an important role in mathematical imaging with many applications in engineering, medicine and art. The TV term is well known to preserve sharp edges in images. More precisely, we are interested in the minimization of a functional formed by a discrepancy term and a TV term. The first order derivat...
متن کاملLocal analysis of discontinuous Galerkin methods applied to singularly perturbed problems
We analyze existing discontinuous Galerkin methods on quasi-uniform meshes for singularly perturbed problems. We prove weighted L2 error estimates. We use the weighted estimates to prove L2 error estimates in regions where the solution is smooth. We also prove pointwise estimates in these regions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Numerical Mathematics
سال: 2004
ISSN: 1570-2820,1569-3953
DOI: 10.1163/156939504323074504