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Nonweak/Strong Solutions of Linear and Nonlinear Hyperbolic and Parabolic Equations Resulting from a Single Conservation Law

This paper presents an investigation of the numerical computations of nonweak/strong solutions of linear and nonlinear hyperbolic and parabolic differential and partial differential equations resulting from a single conservation law using C1p-version least squares finite element formulation (LSFEF) and C11p-version space time least squares finite element formulation (STLSFEF) for stationary and time dependent processes. It is demonstrated that with this approach it is possible to compute nonweak/strong solutions in the sense that the computed solutions possess the same orders of continuity in space and time as the strong solutions and satisfy nonweak (or residual) form of the governing differential equations (GDE's). Other benefits of this approach over weak solutions are also discussed and demonstrated. Stationary and time dependent convection-diffusion and Burgers equations are used as model problems.