Related papers: General Variational Formulas for Abelian Different…
We study deformations of a genus one Riemann surface and of a second order Abelian differential on the surface which preserve the periods of the differential with respect to a chosen canonical homology basis of the surface. We call these…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
We present a variationally separable splitting technique for the generalized-$\alpha$ method for solving parabolic partial differential equations. We develop a technique for a tensor-product mesh which results in a solver with a linear cost…
We give an example of quasiderivatives constructed by random time change, Girsanov's Theorem and Levy's Theorem. As an application, we investigate the smoothness and estimate the derivatives up to second order for the probabilistic solution…
We study variational problems for curves approximated by B-spline curves. We show that, one can obtain discrete Euler-Lagrange equations, for the data describing the approximated curves. Our main application is to the curve completion…
The variational grid generation method is a powerful tool for generating structured convex grids on irregular simply connected domains whose boundary is a polygonal Jordan curve. Several examples that show the accuracy of a difference…
We introduce a very weak space-time variational formulation for the wave equation, prove its well-posedness (even in the case of minimal regularity) and optimal inf-sup stability. Then, we introduce a tensor product-style space-time…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and…
This article focuses on the space-time isogeometric method for a linear time dependent fourth order problem. Using an auxiliary variable, first the problem is split into a system of two second order differential equations and then the…
We consider a length functional for $C^1$ curves of fixed degree in graded manifolds equipped with a Riemannian metric. The first variation of this length functional can be computed only if the curve can be deformed in a suitable sense, and…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave…
The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…
In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
Variational space-time formulations for Partial Differential Equations have been of great interest in the last decades. While it is known that implicit time marching schemes have variational structure, the Galerkin formulation of explicit…
We introduce a multitree-based adaptive wavelet Galerkin algorithm {for} space-time discretized linear parabolic partial differential equations, focusing on time-periodic problems. It is shown that the method converges with the best…
Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and non-conforming Finite Element, Mixed Finite Element and Finite…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…