# On the Convergence of a Finite Element Method for a Nonlinear Hyperbolic Conservation Law

@inproceedings{Johnson2010OnTC, title={On the Convergence of a Finite Element Method for a Nonlinear Hyperbolic Conservation Law}, author={Claes Johnson and Anders Szepessy}, year={2010} }

- Published 2010

We consider a space-time finite element discretization of a time-dependent nonlinear hyperbolic conservation law in one space dimension (Burgers' equation). The finite element method is higher-order accurate and is a Petrov-Galerkin method based on the so-called streamline diffusion modification of the test functions giving added stability. We first prove that if a sequence of finite element solutions converges boundedly almost everywhere (as the mesh size tends to zero) to a function u, then uâ€¦Â CONTINUE READING

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## Convergence of a residual based artificial viscosity finite element method

View 6 Excerpts

Highly Influenced

## Hierarchical Hexahedral Elements for Fluid Dynamic Simulations Using Stabilized Finite Element Methods

View 6 Excerpts

Highly Influenced

#### References

##### Publications referenced by this paper.

Showing 1-10 of 13 references

## DiPerna, "Convergence of approximate solutions to conservation laws," Arch

View 4 Excerpts

Highly Influenced

## Finite Element Methods for First-order Hyperbolic Systems with Particular Emphasis on the Compressible Euler Equations*

View 4 Excerpts

Highly Influenced

## A new finite element formulation for computational fluid dynamics : I . Symmetric forms of the compressible Euler and Navier - Stokes equations and the second law of thermodynamics

## A new finite element formulation for computational fluid dynamics : III . The generalized streamline operator for multi - dimensional advectivediffusive systems , " Comput

## A new finite element formulation for computational fluid dynamics : IV . A discontinuity capturing operator for multidimensional advectivediffusive systems , " Comput

## A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics," Comput

View 3 Excerpts

## A new finite element method for computational fluid dynamics: II. Beyond SUPG," Comput

View 2 Excerpts

## Entropy stable finite element methods for compressible fluids: Application to high Mach number flows with shocks," in Finite Elements for Nonlinear Problems

View 3 Excerpts