# Thirupathi Gudi

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)
• 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 L2 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)
• Numerische Mathematik
• 2009
A unified a posteriori error analysis is derived in extension of Carstensen (NumerMath 100:617–637, 2005) andCarstensen andHu (JNumerMath 107(3):473– 502, 2007) for a wide range of discontinuous Galerkin (dG) finite element methods (FEM), applied to the Laplace, Stokes, and Lamé equations. Two abstract assumptions (A1) and (A2) guarantee the reliability of(More)
In this paper, we develop and analyze C0 penalty methods for the fully nonlinear Monge-Ampère equation det(D2u) = 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)
• J. Sci. Comput.
• 2010
We show that the weakly over-penalized symmetric interior penalty (WOPSIP) method has high intrinsic parallelism. Consider the following model problem: Find u ∈ H 0 (Ω) such that a(u, v) = ∫ Ω fv dx ∀ v ∈ H 0 (Ω), where Ω ⊂ R is a bounded polygonal domain, f ∈ L2(Ω), and a(w, v) = ∫ Ω ∇w · ∇v dx. This problem can be solved by the weakly over-penalized(More)
• Math. Comput.
• 2011
In this paper, we develop and analyze C0 penalty methods for the fully nonlinear Monge-Ampère equation det(D2u) = 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)