Related papers: Galerkin Methods for Complementarity Problems and …
We use a concept of weak asymptotic solution for homogeneous as well as non-homogeneous fractional advection dispersion type equations. Using Legendre scaling functions as basis, a numerical method based on Galerkin approximation is…
The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…
In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm. The discretization method…
In this article a theoretical framework for problems involving fractional equations of hyperbolic type arising in the theory of viscoelasticity is presented. Based on the Galerkin method, a variational problem of the fractionary…
We study two techniques for correcting the geometrical error associated with domain approximation by a polygon. The first was introduced some time ago \cite{bramble1972projection} and leads to a nonsymmetric formulation for Poisson's…
In this study, we examine numerical approximations for 2nd-order linear-nonlinear differential equations with diverse boundary conditions, followed by the residual corrections of the first approximations. We first obtain numerical results…
In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular, we demonstrate that these schemes provide essential…
We develop and analyse a numerical method for the time-fractional nonlocal thermistor problem. By rigorous proofs, some error estimates in different contexts are derived, showing that the combination of the backward differentiation in time…
In this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinley parametrized geometries. The essential ingredients of the methodology are: a Galerkin…
In this paper we establish best approximation property of fully discrete Galerkin solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty(I;W^{1,\infty}(\Om))$ norm. The discretization method…
Although for a number of semilinear stochastic wave equations existence and uniqueness results for corresponding solution processes are known from the literature, these solution processes are typically not explicitly known and numerical…
In many applications of practical interest, solutions of partial differential equation models arise as critical points of an underlying (energy) functional. If such solutions are saddle points, rather than being maxima or minima, then the…
This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty…
The aim of this work is to consider multiscale algorithms for solving PDEs with Galerkin methods on bounded domains. We provide results on convergence and condition numbers. We show how to handle PDEs with Dirichlet boundary conditions. We…
The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral…
We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension…
We propose an discontinuous Galerkin local orthogonal decomposition multiscale method for convection-diffusion problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the…
Certain Petrov-Galerkin schemes are inherently stable formulations of variational problems on a given mesh. This stability is primarily obtained by computing an optimal test basis for a given approximation space. Furthermore, these…
We apply polynomial approximation methods -- known in the numerical PDEs context as spectral methods -- to approximate the vector-valued function that satisfies a linear system of equations where the matrix and the right hand side depend on…
We devise and analyze a class of interior penalty discontinuous Galerkin methods for nonlinear and nonsmooth variational problems. Discrete duality relations are derived that lead to optimal error estimates in the case of total-variation…