Thirupathi Gudi

Learn More
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)
We study a weakly over-penalized symmetric interior penalty method for the biharmonic problem that is intrinsically parallel. Both a priori error analysis and a posteriori error analysis are carried out. The performance of the method is illustrated by numerical experiments. 1. Introduction. Recently, it was noted in [9] that the Poisson problem can be(More)
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)
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 first split the biharmonic equation !2u = f with nonhomogeneous 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 vh of v can easily be eliminated to reduce the(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)
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)
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)
A WEAKLY OVER-PENALIZED SYMMETRIC INTERIOR PENALTY METHOD SUSANNE C. BRENNER , LUKE OWENS , AND LI-YENG SUNG Abstract. We introduce a new symmetric interior penalty method for symmetric positive definite second order elliptic boundary value problems, where the jumps across element boundaries are weakly over-penalized. Error estimates are derived in the(More)