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- Thirupathi Gudi
- Math. Comput.
- 2010

The standard a priori error analysis of discontinuous Galerkin methods requires additional regularity on the solution of the elliptic boundary value problem in order to justify the Galerkin orthogonality and to handle the normal derivative on element interfaces that appear in the discrete energy norm. In this paper, a new error analysis of discontinuous… (More)

Let Ω ⊂ R 2 be a bounded polygonal domain, f ∈ L 2 (Ω) and ϕ ∈ H 2 (Ω). Consider the model problem of finding u ∈ H 1 (Ω) such that −∆u = f in Ω, (1a) u = ϕ on ∂Ω. (1b) In this talk we discuss a weakly over-penalized symmetric interior penalty (WOPSIP) method for (1) introduced in [1,2]. Let T h be a simplicial triangulation of Ω and V h be the… (More)

- Carsten Carstensen, Thirupathi Gudi, Max Jensen
- Numerische Mathematik
- 2009

- Susanne C. Brenner, Thirupathi Gudi, Michael Neilan, Li-Yeng Sung
- Math. Comput.
- 2011

In this paper, we develop and analyze C 0 penalty methods for the fully nonlinear Monge-Ampère equation det(D 2 u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the… (More)

- Thirupathi Gudi, Neela Nataraj, Amiya Kumar Pani
- J. Sci. Comput.
- 2008

In this paper, we first split the biharmonic equation 2 u = f with nonhomoge-neous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v = u and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation v h of v can easily be eliminated to reduce the… (More)

- Susanne C. Brenner, Jintao Cui, Thirupathi Gudi, Li-Yeng Sung
- Numerische Mathematik
- 2011

We study a class of symmetric discontinuous Galerkin methods on graded meshes. Optimal order error estimates are derived in both the energy norm and the L 2 norm, and we establish the uniform convergence of V-cycle, F-cycle and W-cycle multigrid algorithms for the resulting discrete problems. Numerical results that confirm the theoretical results are also… (More)

- Susanne C. Brenner, Thirupathi Gudi, Luke Owens, Li-Yeng Sung
- J. Sci. Comput.
- 2010

- Susanne C. Brenner, Shiyuan Gu, Thirupathi Gudi, Li-Yeng Sung
- SIAM J. Numerical Analysis
- 2012

- Thirupathi Gudi, Neela Nataraj, Amiya Kumar Pani
- Math. Comput.
- 2008

In this paper, an hp-local discontinuous Galerkin method is applied to a class of quasilinear elliptic boundary value problems which are of nonmonotone type. On hp-quasiuniform meshes, using the Brouwer fixed point theorem, it is shown that the discrete problem has a solution, and then using Lipschitz continuity of the discrete solution map, uniqueness is… (More)

- Thirupathi Gudi, Amiya Kumar Pani
- SIAM J. Numerical Analysis
- 2007